Index

A (appendix), 1
A (archetype), 2
A (definition), 3
A (notation), 4
A (part), 5
AA (Property), 6
AA (subsection, section WILA), 7
AA (theorem), 8
AAC (Property), 9
AACN (Property), 10
AAF (Property), 11
AALC (example), 12
AAM (Property), 13
ABLC (example), 14
ABS (example), 15
AC (Property), 16
ACC (Property), 17
ACCN (Property), 18
ACF (Property), 19, 20
ACM (Property), 21
ACN (example), 22
additive associativity
    column vectors
        Property AAC, 23
    complex numbers
        Property AACN, 24
    matrices
        Property AAM, 25
    vectors
        Property AA, 26
additive commutativity
    complex numbers
        Property ACCN, 27
additive inverse
    complex numbers
        Property AICN, 28
    from scalar multiplication
        theorem AISM, 29
additive inverses
    column vectors
        Property AIC, 30
    matrices
        Property AIM, 31
    unique
        theorem AIU, 32
    vectors
        Property AI, 33
addtive closure
    column vectors
        Property ACC, 34
    field
        Property ACF, 35
    matrices
        Property ACM, 36
    vectors
        Property AC, 37
adjoint
    definition A, 38
    inner product
        theorem AIP, 39
    notation, 40
    of a matrix sum
        theorem AMA, 41
    of an adjoint
        theorem AA, 42
    of matrix scalar multiplication
        theorem AMSM, 43
AHSAC (example), 44
AI (Property), 45
AIC (Property), 46
AICN (Property), 47
AIF (Property), 48
AIM (Property), 49
AIP (theorem), 50
AISM (theorem), 51
AIU (theorem), 52
AIVLT (example), 53
ALT (example), 54
ALTMM (example), 55
AM (definition), 56
AM (example), 57
AM (notation), 58
AM (subsection, section MO), 59
AMA (theorem), 60
AMAA (example), 61
AME (definition), 62
AMSM (theorem), 63
ANILT (example), 64
ANM (example), 65
AOS (example), 66
Archetype A
    column space, 67
    linearly dependent columns, 68
    singular matrix, 69
    solving homogeneous system, 70
    system as linear combination, 71
archetype A
    augmented matrix
        example AMAA, 72
Archetype B
    column space, 73
    inverse
        example CMIAB, 74
    linearly independent columns, 75
    nonsingular matrix, 76
    not invertible
        example MWIAA, 77
    solutions via inverse
        example SABMI, 78
    solving homogeneous system, 79
    system as linear combination, 80
    vector equality, 81
archetype B
    solutions
        example SAB, 82
Archetype C
    homogeneous system, 83
Archetype D
    column space, original columns, 84
    solving homogeneous system, 85
    vector form of solutions, 86
Archetype I
    column space from row operations, 87
    null space, 88
    row space, 89
    vector form of solutions, 90
Archetype I:casting out vectors, 91
Archetype L
    null space span, linearly independent, 92
    vector form of solutions, 93
ASC (example), 94
augmented matrix
    notation, 95
AVR (example), 96

B (archetype), 97
B (definition), 98
B (section), 99
B (subsection, section B), 100
basis
    columns nonsingular matrix
        example CABAK, 101
    common size
        theorem BIS, 102
    crazy vector apace
        example BC, 103
    definition B, 104
    matrices
        example BM, 105
        example BSM22, 106
    polynomials
        example BP, 107
        example BPR, 108
        example BSP4, 109
        example SVP4, 110
    subspace of matrices
        example BDM22, 111
BC (example), 112
BCS (theorem), 113
BDE (example), 114
BDM22 (example), 115
best cities
    money magazine
        example MBC, 116
BIS (theorem), 117
BM (example), 118
BNM (subsection, section B), 119
BNS (theorem), 120
BP (example), 121
BPR (example), 122
BRLT (example), 123
BRS (theorem), 124
BS (theorem), 125
BSCV (subsection, section B), 126
BSM22 (example), 127
BSP4 (example), 128

C (archetype), 129
C (definition), 130
C (notation), 131
C (part), 132
C (Property), 133
C (technique, section PT), 134
CABAK (example), 135
CAEHW (example), 136
canonical form
    nilpotent linear transformation
        example CFNLT, 137
        theorem CFNLT, 138
CAV (subsection, section O), 139
Cayley-Hamilton
    theorem CHT, 140
CB (section), 141
CB (theorem), 142
CBCV (example), 143
CBM (definition), 144
CBM (subsection, section CB), 145
CBOB (theorem), 146
CBP (example), 147
CC (Property), 148
CCCV (definition), 149
CCCV (notation), 150
CCM (definition), 151
CCM (example), 152
CCM (notation), 153
CCM (theorem), 154
CCN (definition), 155
CCN (notation), 156
CCN (subsection, section CNO), 157
CCRA (theorem), 158
CCRM (theorem), 159
CCT (theorem), 160
CD (subsection, section DM), 161
CD (technique, section PT), 162
CEE (subsection, section EE), 163
CELT (example), 164
CELT (subsection, section CB), 165
CEMS6 (example), 166
CF (section), 167
CFDVS (theorem), 168
CFNLT (example), 169
CFNLT (subsection, section NLT), 170
CFNLT (theorem), 171
CFV (example), 172
change of basis
    between polynomials
        example CBP, 173
change-of-basis
    between column vectors
        example CBCV, 174
    matrix representation
        theorem MRCB, 175
    similarity
        theorem SCB, 176
    theorem CB, 177
change-of-basis matrix
    definition CBM, 178
    inverse
        theorem ICBM, 179
characteristic polynomial
    definition CP, 180
    degree
        theorem DCP, 181
    size 3 matrix
        example CPMS3, 182
CHT (subsection, section JCF), 183
CHT (theorem), 184
CILT (subsection, section ILT), 185
CILTI (theorem), 186
CIM (subsection, section MISLE), 187
CINM (theorem), 188
CIVLT (theorem), 189
CLI (theorem), 190
CLTLT (theorem), 191
CM (definition), 192
CM (Property), 193
CM32 (example), 194
CMI (example), 195
CMIAB (example), 196
CMVEI (theorem), 197
CN (appendix), 198
CNA (definition), 199
CNA (notation), 200
CNA (subsection, section CNO), 201
CNE (definition), 202
CNE (notation), 203
CNM (definition), 204
CNM (notation), 205
CNMB (theorem), 206
CNO (section), 207
CNS1 (example), 208
CNS2 (example), 209
CNSV (example), 210
COB (theorem), 211
coefficient matrix
    definition CM, 212
    nonsingular
        theorem SNCM, 213
column space
    as null space
        theorem FS, 214
    Archetype A
        example CSAA, 215
    Archetype B
        example CSAB, 216
    as null space
        example CSANS, 217
    as null space, Archetype G
        example FSAG, 218
    as row space
        theorem CSRST, 219
    basis
        theorem BCS, 220
    consistent system
        theorem CSCS, 221
    consistent systems
        example CSMCS, 222
    isomorphic to range, 223
    matrix, 224
    nonsingular matrix
        theorem CSNM, 225
    notation, 226
    original columns, Archetype D
        example CSOCD, 227
    row operations, Archetype I
        example CSROI, 228
    subspace
        theorem CSMS, 229
    testing membership
        example MCSM, 230
    two computations
        example CSTW, 231
column vector addition
    notation, 232
column vector scalar multiplication
    notation, 233
commutativity
    column vectors
        Property CC, 234
    matrices
        Property CM, 235
    vectors
        Property C, 236
complex m-space
    example VSCV, 237
complex arithmetic
    example ACN, 238
complex number
    conjugate
        example CSCN, 239
    modulus
        example MSCN, 240
complex number
    conjugate
        definition CCN, 241
    modulus
        definition MCN, 242
complex numbers
    addition
        definition CNA, 243
        notation, 244
    arithmetic properties
        theorem PCNA, 245
    equality
        definition CNE, 246
        notation, 247
    multiplication
        definition CNM, 248
        notation, 249
complex vector space
    dimension
        theorem DCM, 250
composition
    injective linear transformations
        theorem CILTI, 251
    surjective linear transformations
        theorem CSLTS, 252
conjugate
    addition
        theorem CCRA, 253
    column vector
        definition CCCV, 254
    matrix
        definition CCM, 255
        notation, 256
    multiplication
        theorem CCRM, 257
    notation, 258
    of conjugate of a matrix
        theorem CCM, 259
    scalar multiplication
        theorem CRSM, 260
    twice
        theorem CCT, 261
    vector addition
        theorem CRVA, 262
conjugate of a vector
    notation, 263
conjugation
    matrix addition
        theorem CRMA, 264
    matrix scalar multiplication
        theorem CRMSM, 265
    matrix transpose
        theorem MCT, 266
consistent linear system, 267
consistent linear systems
    theorem CSRN, 268
consistent system
    definition CS, 269
constructive proofs
    technique C, 270
contradiction
    technique CD, 271
contrapositive
    technique CP, 272
converse
    technique CV, 273
coordinates
    orthonormal basis
        theorem COB, 274
coordinatization
    linear combination of matrices
        example CM32, 275
    linear independence
        theorem CLI, 276
    orthonormal basis
        example CROB3, 277
        example CROB4, 278
    spanning sets
        theorem CSS, 279
coordinatization principle, 280
coordinatizing
    polynomials
        example CP2, 281
COV (example), 282
COV (subsection, section LDS), 283
CP (definition), 284
CP (subsection, section VR), 285
CP (technique, section PT), 286
CP2 (example), 287
CPMS3 (example), 288
CPSM (theorem), 289
crazy vector space
    example CVSR, 290
    properties
        example PCVS, 291
CRMA (theorem), 292
CRMSM (theorem), 293
CRN (theorem), 294
CROB3 (example), 295
CROB4 (example), 296
CRS (section), 297
CRS (subsection, section FS), 298
CRSM (theorem), 299
CRVA (theorem), 300
CS (definition), 301
CS (example), 302
CS (subsection, section TSS), 303
CSAA (example), 304
CSAB (example), 305
CSANS (example), 306
CSCN (example), 307
CSCS (theorem), 308
CSIP (example), 309
CSLT (subsection, section SLT), 310
CSLTS (theorem), 311
CSM (definition), 312
CSM (notation), 313
CSMCS (example), 314
CSMS (theorem), 315
CSNM (subsection, section CRS), 316
CSNM (theorem), 317
CSOCD (example), 318
CSRN (theorem), 319
CSROI (example), 320
CSRST (theorem), 321
CSS (theorem), 322
CSSE (subsection, section CRS), 323
CSSOC (subsection, section CRS), 324
CSTW (example), 325
CTD (subsection, section TD), 326
CTLT (example), 327
CUMOS (theorem), 328
curve fitting
    polynomial through 5 points
        example PTFP, 329
CV (definition), 330
CV (notation), 331
CV (technique, section PT), 332
CVA (definition), 333
CVA (notation), 334
CVC (notation), 335
CVE (definition), 336
CVE (notation), 337
CVS (example), 338
CVS (subsection, section VR), 339
CVSM (definition), 340
CVSM (example), 341
CVSM (notation), 342
CVSR (example), 343

D (archetype), 344
D (chapter), 345
D (definition), 346
D (notation), 347
D (section), 348
D (subsection, section D), 349
D (subsection, section SD), 350
D (technique, section PT), 351
D33M (example), 352
DAB (example), 353
DC (example), 354
DC (technique, section PT), 355
DC (theorem), 356
DCM (theorem), 357
DCN (Property), 358
DCP (theorem), 359
DD (subsection, section DM), 360
DEC (theorem), 361
decomposition
    technique DC, 362
DED (theorem), 363
definition
    A, 364
    AM, 365
    AME, 366
    B, 367
    C, 368
    CBM, 369
    CCCV, 370
    CCM, 371
    CCN, 372
    CM, 373
    CNA, 374
    CNE, 375
    CNM, 376
    CP, 377
    CS, 378
    CSM, 379
    CV, 380
    CVA, 381
    CVE, 382
    CVSM, 383
    D, 384
    DIM, 385
    DM, 386
    DS, 387
    DZM, 388
    EEF, 389
    EELT, 390
    EEM, 391
    ELEM, 392
    EM, 393
    EO, 394
    ES, 395
    ESYS, 396
    F, 397
    GES, 398
    GEV, 399
    GME, 400
    HM, 401
    HS, 402
    IDLT, 403
    IDV, 404
    IE, 405
    ILT, 406
    IM, 407
    IMP, 408
    IP, 409
    IS, 410
    IVLT, 411
    IVS, 412
    JB, 413
    JCF, 414
    KLT, 415
    LC, 416
    LCCV, 417
    LI, 418
    LICV, 419
    LNS, 420
    LSMR, 421
    LSS, 422
    LT, 423
    LTA, 424
    LTC, 425
    LTM, 426
    LTR, 427
    LTSM, 428
    M, 429
    MA, 430
    MCN, 431
    ME, 432
    MI, 433
    MM, 434
    MR, 435
    MSM, 436
    MVP, 437
    NLT, 438
    NM, 439
    NOLT, 440
    NOM, 441
    NRML, 442
    NSM, 443
    NV, 444
    ONS, 445
    OSV, 446
    OV, 447
    PI, 448
    PSM, 449
    REM, 450
    RLD, 451
    RLDCV, 452
    RLT, 453
    RO, 454
    ROLT, 455
    ROM, 456
    RR, 457
    RREF, 458
    RSM, 459
    S, 460
    SC, 461
    SE, 462
    SET, 463
    SI, 464
    SIM, 465
    SLE, 466
    SLT, 467
    SM, 468
    SQM, 469
    SRM, 470
    SS, 471
    SSCV, 472
    SSET, 473
    SU, 474
    SUV, 475
    SV, 476, 477
    SYM, 478
    T, 479
    technique D, 480
    TM, 481
    TS, 482
    TSHSE, 483
    TSVS, 484
    UM, 485
    UTM, 486
    VM, 487
    VOC, 488
    VR, 489
    VS, 490
    VSCV, 491
    VSM, 492
    ZCV, 493
    ZM, 494
DEHD (example), 495
DEM (theorem), 496
DEMMM (theorem), 497
DEMS5 (example), 498
DER (theorem), 499
DERC (theorem), 500
determinant
    computed two ways
        example TCSD, 501
    definition DM, 502
    equal rows or columns
        theorem DERC, 503
    expansion, columns
        theorem DEC, 504
    expansion, rows
        theorem DER, 505
    identity matrix
        theorem DIM, 506
    matrix multiplication
        theorem DRMM, 507
    nonsingular matrix, 508
    notation, 509
    row or column multiple
        theorem DRCM, 510
    row or column swap
        theorem DRCS, 511
    size 2 matrix
        theorem DMST, 512
    size 3 matrix
        example D33M, 513
    transpose
        theorem DT, 514
    via row operations
        example DRO, 515
    zero
        theorem SMZD, 516
    zero row or column
        theorem DZRC, 517
    zero versus nonzero
        example ZNDAB, 518
determinant, upper triangular matrix
    example DUTM, 519
determinants
    elementary matrices
        theorem DEMMM, 520
DF (Property), 521
DF (subsection, section CF), 522
DFS (subsection, section PD), 523
DFS (theorem), 524
DGES (theorem), 525
diagonal matrix
    definition DIM, 526
diagonalizable
    definition DZM, 527
    distinct eigenvalues
        example DEHD, 528
        theorem DED, 529
    full eigenspaces
        theorem DMFE, 530
    not
        example NDMS4, 531
diagonalizable matrix
    high power
        example HPDM, 532
diagonalization
    Archetype B
        example DAB, 533
    criteria
        theorem DC, 534
    example DMS3, 535
DIM (definition), 536
DIM (theorem), 537
dimension
    crazy vector space
        example DC, 538
    definition D, 539
    notation, 540
    polynomial subspace
        example DSP4, 541
    proper subspaces
        theorem PSSD, 542
    subspace
        example DSM22, 543
direct sum
    decomposing zero vector
        theorem DSZV, 544
    definition DS, 545
    dimension
        theorem DSD, 546
    example SDS, 547
    from a basis
        theorem DSFB, 548
    from one subspace
        theorem DSFOS, 549
    notation, 550
    zero intersection
        theorem DSZI, 551
direct sums
    linear independence
        theorem DSLI, 552
    repeated
        theorem RDS, 553
distributivity
    complex numbers
        Property DCN, 554
    field
        Property DF, 555
distributivity, matrix addition
    matrices
        Property DMAM, 556
distributivity, scalar addition
    column vectors
        Property DSAC, 557
    matrices
        Property DSAM, 558
    vectors
        Property DSA, 559
distributivity, vector addition
    column vectors
        Property DVAC, 560
    vectors
        Property DVA, 561
DLDS (theorem), 562
DM (definition), 563
DM (notation), 564
DM (section), 565
DM (theorem), 566
DMAM (Property), 567
DMFE (theorem), 568
DMS3 (example), 569
DMST (theorem), 570
DNLT (theorem), 571
DNMMM (subsection, section PDM), 572
DP (theorem), 573
DRCM (theorem), 574
DRCMA (theorem), 575
DRCS (theorem), 576
DRMM (theorem), 577
DRO (example), 578
DRO (subsection, section PDM), 579
DROEM (subsection, section PDM), 580
DS (definition), 581
DS (notation), 582
DS (subsection, section PD), 583
DSA (Property), 584
DSAC (Property), 585
DSAM (Property), 586
DSD (theorem), 587
DSFB (theorem), 588
DSFOS (theorem), 589
DSLI (theorem), 590
DSM22 (example), 591
DSP4 (example), 592
DSZI (theorem), 593
DSZV (theorem), 594
DT (theorem), 595
DUTM (example), 596
DVA (Property), 597
DVAC (Property), 598
DVM (theorem), 599
DVS (subsection, section D), 600
DZM (definition), 601
DZRC (theorem), 602

E (archetype), 603
E (chapter), 604
E (technique, section PT), 605
ECEE (subsection, section EE), 606
EDELI (theorem), 607
EDYES (theorem), 608
EE (section), 609
EEE (subsection, section EE), 610
EEF (definition), 611
EEF (subsection, section FS), 612
EELT (definition), 613
EELT (subsection, section CB), 614
EEM (definition), 615
EEM (subsection, section EE), 616
EEMAP (theorem), 617
EENS (example), 618
EER (theorem), 619
EESR (theorem), 620
EHM (subsection, section PEE), 621
eigenspace
    as null space
        theorem EMNS, 622
    definition EM, 623
    invariant subspace
        theorem EIS, 624
    subspace
        theorem EMS, 625
eigenvalue
    algebraic multiplicity
        definition AME, 626
    complex
        example CEMS6, 627
    definition EEM, 628
    existence
        example CAEHW, 629
        theorem EMHE, 630
    geometric multiplicity
        definition GME, 631
    index, 632
    linear transformation
        definition EELT, 633
    multiplicities
        example EMMS4, 634
    power
        theorem EOMP, 635
    root of characteristic polynomial
        theorem EMRCP, 636
    scalar multiple
        theorem ESMM, 637
    symmetric matrix
        example ESMS4, 638
    zero
        theorem SMZE, 639
eigenvalues
    building desired
        example BDE, 640
    complex, of a linear transformation
        example CELT, 641
    conjugate pairs
        theorem ERMCP, 642
    distinct
        example DEMS5, 643
    example SEE, 644
    Hermitian matrices
        theorem HMRE, 645
    inverse
        theorem EIM, 646
    maximum number
        theorem MNEM, 647
    multiplicities
        example HMEM5, 648
        theorem ME, 649
    number
        theorem NEM, 650
    of a polynomial
        theorem EPM, 651
    size 3 matrix
        example EMS3, 652
        example ESMS3, 653
    transpose
        theorem ETM, 654
eigenvalues, eigenvectors
    vector, matrix representations
        theorem EER, 655
eigenvector, 656
    linear transformation, 657
eigenvectors, 658
    conjugate pairs, 659
    Hermitian matrices
        theorem HMOE, 660
    linear transformation
        example ELTBM, 661
        example ELTBP, 662
    linearly independent
        theorem EDELI, 663
    of a linear transformation
        example ELTT, 664
EILT (subsection, section ILT), 665
EIM (theorem), 666
EIS (example), 667
EIS (theorem), 668
ELEM (definition), 669
ELEM (notation), 670
elementary matrices
    definition ELEM, 671
    determinants
        theorem DEM, 672
    nonsingular
        theorem EMN, 673
    notation, 674
    row operations
        example EMRO, 675
        theorem EMDRO, 676
ELIS (theorem), 677
ELTBM (example), 678
ELTBP (example), 679
ELTT (example), 680
EM (definition), 681
EM (subsection, section DM), 682
EMDRO (theorem), 683
EMHE (theorem), 684
EMMS4 (example), 685
EMMVP (theorem), 686
EMN (theorem), 687
EMNS (theorem), 688
EMP (theorem), 689
empty set, 690
    notation, 691
EMRCP (theorem), 692
EMRO (example), 693
EMS (theorem), 694
EMS3 (example), 695
ENLT (theorem), 696
EO (definition), 697
EOMP (theorem), 698
EOPSS (theorem), 699
EPM (theorem), 700
EPSM (theorem), 701
equal matrices
    via equal matrix-vector products
        theorem EMMVP, 702
equation operations
    definition EO, 703
    theorem EOPSS, 704
equivalence statements
    technique E, 705
equivalences
    technique ME, 706
equivalent systems
    definition ESYS, 707
ERMCP (theorem), 708
ES (definition), 709
ES (notation), 710
ESEO (subsection, section SSLE), 711
ESLT (subsection, section SLT), 712
ESMM (theorem), 713
ESMS3 (example), 714
ESMS4 (example), 715
ESYS (definition), 716
ETM (theorem), 717
EVS (subsection, section VS), 718
example
    AALC, 719
    ABLC, 720
    ABS, 721
    ACN, 722
    AHSAC, 723
    AIVLT, 724
    ALT, 725
    ALTMM, 726
    AM, 727
    AMAA, 728
    ANILT, 729
    ANM, 730
    AOS, 731
    ASC, 732
    AVR, 733
    BC, 734
    BDE, 735
    BDM22, 736
    BM, 737
    BP, 738
    BPR, 739
    BRLT, 740
    BSM22, 741
    BSP4, 742
    CABAK, 743
    CAEHW, 744
    CBCV, 745
    CBP, 746
    CCM, 747
    CELT, 748
    CEMS6, 749
    CFNLT, 750
    CFV, 751
    CM32, 752
    CMI, 753
    CMIAB, 754
    CNS1, 755
    CNS2, 756
    CNSV, 757
    COV, 758
    CP2, 759
    CPMS3, 760
    CROB3, 761
    CROB4, 762
    CS, 763
    CSAA, 764
    CSAB, 765
    CSANS, 766
    CSCN, 767
    CSIP, 768
    CSMCS, 769
    CSOCD, 770
    CSROI, 771
    CSTW, 772
    CTLT, 773
    CVS, 774
    CVSM, 775
    CVSR, 776
    D33M, 777
    DAB, 778
    DC, 779
    DEHD, 780
    DEMS5, 781
    DMS3, 782
    DRO, 783
    DSM22, 784
    DSP4, 785
    DUTM, 786
    EENS, 787
    EIS, 788
    ELTBM, 789
    ELTBP, 790
    ELTT, 791
    EMMS4, 792
    EMRO, 793
    EMS3, 794
    ESMS3, 795
    ESMS4, 796
    FDV, 797
    FF8, 798
    FRAN, 799
    FS1, 800
    FS2, 801
    FSAG, 802
    GE4, 803
    GE6, 804
    GENR6, 805
    GSTV, 806
    HISAA, 807
    HISAD, 808
    HMEM5, 809
    HPDM, 810
    HUSAB, 811
    IAP, 812
    IAR, 813
    IAS, 814
    IAV, 815
    ILTVR, 816
    IM, 817
    IM11, 818
    IS, 819
    ISJB, 820
    ISMR4, 821
    ISMR6, 822
    ISSI, 823
    IVSAV, 824
    JB4, 825
    JCF10, 826
    KPNLT, 827
    KVMR, 828
    LCM, 829
    LDCAA, 830
    LDHS, 831
    LDP4, 832
    LDRN, 833
    LDS, 834
    LIC, 835
    LICAB, 836
    LIHS, 837
    LIM32, 838
    LINSB, 839
    LIP4, 840
    LIS, 841
    LLDS, 842
    LNS, 843
    LTDB1, 844
    LTDB2, 845
    LTDB3, 846
    LTM, 847
    LTPM, 848
    LTPP, 849
    LTRGE, 850
    MA, 851
    MBC, 852
    MCSM, 853
    MFLT, 854
    MI, 855
    MIVS, 856
    MMNC, 857
    MNSLE, 858
    MOLT, 859
    MPMR, 860
    MRBE, 861
    MRCM, 862
    MSCN, 863
    MSM, 864
    MTV, 865
    MWIAA, 866
    NDMS4, 867
    NIAO, 868
    NIAQ, 869
    NIAQR, 870
    NIDAU, 871
    NJB5, 872
    NKAO, 873
    NLT, 874
    NM, 875
    NM62, 876
    NM64, 877
    NM83, 878
    NRREF, 879
    NSAO, 880
    NSAQ, 881
    NSAQR, 882
    NSC2A, 883
    NSC2S, 884
    NSC2Z, 885
    NSDAT, 886
    NSDS, 887
    NSE, 888
    NSEAI, 889
    NSLE, 890
    NSLIL, 891
    NSNM, 892
    NSR, 893
    NSS, 894
    OLTTR, 895
    ONFV, 896
    ONTV, 897
    OSGMD, 898
    OSMC, 899
    PCVS, 900
    PM, 901
    PSHS, 902
    PTFP, 903
    PTM, 904
    PTMEE, 905
    RAO, 906
    RES, 907
    RNM, 908
    RNSM, 909
    ROD2, 910
    ROD4, 911
    RREF, 912
    RREFN, 913
    RRTI, 914
    RS, 915
    RSAI, 916
    RSB, 917
    RSC5, 918
    RSNS, 919
    RSREM, 920
    RSSC4, 921
    RVMR, 922
    S, 923
    SAA, 924
    SAB, 925
    SABMI, 926
    SAE, 927
    SAN, 928
    SAR, 929
    SAV, 930
    SC, 931
    SC3, 932
    SCAA, 933
    SCAB, 934
    SCAD, 935
    SDS, 936
    SEE, 937
    SEEF, 938
    SETM, 939
    SI, 940
    SM2Z7, 941
    SM32, 942
    SMLT, 943
    SMS3, 944
    SMS5, 945
    SP4, 946
    SPIAS, 947
    SRR, 948
    SS, 949
    SS6W, 950
    SSC, 951
    SSET, 952
    SSM22, 953
    SSNS, 954
    SSP, 955
    SSP4, 956
    STLT, 957
    STNE, 958
    SU, 959
    SUVOS, 960
    SVP4, 961
    SYM, 962
    TCSD, 963
    TD4, 964
    TDEE6, 965
    TDSSE, 966
    TIS, 967
    TIVS, 968
    TKAP, 969
    TLC, 970
    TM, 971
    TMP, 972
    TOV, 973
    TREM, 974
    TTS, 975
    UM3, 976
    UPM, 977
    US, 978
    USR, 979
    VA, 980
    VESE, 981
    VFS, 982
    VFSAD, 983
    VFSAI, 984
    VFSAL, 985
    VM4, 986
    VRC4, 987
    VRP2, 988
    VSCV, 989
    VSF, 990
    VSIM5, 991
    VSIS, 992
    VSM, 993
    VSP, 994
    VSPUD, 995
    VSS, 996
    ZNDAB, 997
EXC (subsection, section B), 998
EXC (subsection, section CB), 999
EXC (subsection, section CF), 1000
EXC (subsection, section CRS), 1001
EXC (subsection, section D), 1002
EXC (subsection, section DM), 1003
EXC (subsection, section EE), 1004
EXC (subsection, section F), 1005
EXC (subsection, section FS), 1006
EXC (subsection, section HSE), 1007
EXC (subsection, section ILT), 1008
EXC (subsection, section IVLT), 1009
EXC (subsection, section LC), 1010
EXC (subsection, section LDS), 1011
EXC (subsection, section LI), 1012
EXC (subsection, section LISS), 1013
EXC (subsection, section LT), 1014
EXC (subsection, section MINM), 1015
EXC (subsection, section MISLE), 1016
EXC (subsection, section MM), 1017
EXC (subsection, section MO), 1018
EXC (subsection, section MR), 1019
EXC (subsection, section NM), 1020
EXC (subsection, section O), 1021
EXC (subsection, section PD), 1022
EXC (subsection, section PDM), 1023
EXC (subsection, section PEE), 1024
EXC (subsection, section PSM), 1025
EXC (subsection, section RREF), 1026
EXC (subsection, section S), 1027
EXC (subsection, section SD), 1028
EXC (subsection, section SLT), 1029
EXC (subsection, section SS), 1030
EXC (subsection, section SSLE), 1031
EXC (subsection, section T), 1032
EXC (subsection, section TSS), 1033
EXC (subsection, section VO), 1034
EXC (subsection, section VR), 1035
EXC (subsection, section VS), 1036
EXC (subsection, section WILA), 1037
extended echelon form
    submatrices
        example SEEF, 1038
extended reduced row-echelon form
    properties
        theorem PEEF, 1039

F (archetype), 1040
F (definition), 1041
F (section), 1042
F (subsection, section F), 1043
FDV (example), 1044
FF (subsection, section F), 1045
FF8 (example), 1046
field
    definition F, 1047
FIMP (theorem), 1048
finite field
    size 8
        example FF8, 1049
four subsets
    example FS1, 1050
    example FS2, 1051
four subspaces
    dimension
        theorem DFS, 1052
FRAN (example), 1053
free variables
    example CFV, 1054
free variables, number
    theorem FVCS, 1055
free, independent variables
    example FDV, 1056
FS (section), 1057
FS (subsection, section FS), 1058
FS (theorem), 1059
FS1 (example), 1060
FS2 (example), 1061
FSAG (example), 1062
FTMR (theorem), 1063
FV (subsection, section TSS), 1064
FVCS (theorem), 1065

G (archetype), 1066
G (theorem), 1067
GE4 (example), 1068
GE6 (example), 1069
GEE (subsection, section IS), 1070
GEK (theorem), 1071
generalized eigenspace
    as kernel
        theorem GEK, 1072
    definition GES, 1073
    dimension
        theorem DGES, 1074
    dimension 4 domain
        example GE4, 1075
    dimension 6 domain
        example GE6, 1076
    invariant subspace
        theorem GESIS, 1077
    nilpotent restriction
        theorem RGEN, 1078
    nilpotent restrictions, dimension 6 domain
        example GENR6, 1079
    notation, 1080
generalized eigenspace decomposition
    theorem GESD, 1081
generalized eigenvector
    definition GEV, 1082
GENR6 (example), 1083
GES (definition), 1084
GES (notation), 1085
GESD (subsection, section JCF), 1086
GESD (theorem), 1087
GESIS (theorem), 1088
GEV (definition), 1089
GFDL (appendix), 1090
GME (definition), 1091
goldilocks
    theorem G, 1092
Gram-Schmidt
    column vectors
        theorem GSP, 1093
    three vectors
        example GSTV, 1094
gram-schmidt
    mathematica, 1095
GS (technique, section PT), 1096
GSP (subsection, section O), 1097
GSP (theorem), 1098
GSP.MMA (computation, section MMA), 1099
GSTV (example), 1100
GT (subsection, section PD), 1101

H (archetype), 1102
hermitian
    definition HM, 1103
Hermitian matrix
    inner product
        theorem HMIP, 1104
HISAA (example), 1105
HISAD (example), 1106
HM (definition), 1107
HM (subsection, section MM), 1108
HMEM5 (example), 1109
HMIP (theorem), 1110
HMOE (theorem), 1111
HMRE (theorem), 1112
HMVEI (theorem), 1113
homogeneous system
    consistent
        theorem HSC, 1114
    definition HS, 1115
    infinitely many solutions
        theorem HMVEI, 1116
homogeneous systems
    linear independence, 1117
homogenous system
    Archetype C
        example AHSAC, 1118
HPDM (example), 1119
HS (definition), 1120
HSC (theorem), 1121
HSE (section), 1122
HUSAB (example), 1123

I (archetype), 1124
I (technique, section PT), 1125
IAP (example), 1126
IAR (example), 1127
IAS (example), 1128
IAV (example), 1129
ICBM (theorem), 1130
ICLT (theorem), 1131
identities
    technique PI, 1132
identity matrix
    determinant, 1133
    example IM, 1134
    notation, 1135
IDLT (definition), 1136
IDV (definition), 1137
IE (definition), 1138
IE (notation), 1139
IFDVS (theorem), 1140
IILT (theorem), 1141
ILT (definition), 1142
ILT (section), 1143
ILTB (theorem), 1144
ILTD (subsection, section ILT), 1145
ILTD (theorem), 1146
ILTIS (theorem), 1147
ILTLI (subsection, section ILT), 1148
ILTLI (theorem), 1149
ILTLT (theorem), 1150
ILTVR (example), 1151
IM (definition), 1152
IM (example), 1153
IM (notation), 1154
IM (subsection, section MISLE), 1155
IM11 (example), 1156
IMILT (theorem), 1157
IMP (definition), 1158
IMR (theorem), 1159
inconsistent linear systems
    theorem ISRN, 1160
independent, dependent variables
    definition IDV, 1161
indesxstring
    example SM2Z7, 1162
    example SSET, 1163
index
    eigenvalue
        definition IE, 1164
        notation, 1165
indexstring
    theorem CBOB, 1166
    theorem DRCMA, 1167
    theorem OBUTR, 1168
    theorem UMCOB, 1169
induction
    technique I, 1170
infinite solution set
    example ISSI, 1171
infinite solutions, 3 × 4
    example IS, 1172
injective
    example IAP, 1173
    example IAR, 1174
    not
        example NIAO, 1175
        example NIAQ, 1176
        example NIAQR, 1177
    not, by dimension
        example NIDAU, 1178
    polynomials to matrices
        example IAV, 1179
injective linear transformation
    bases
        theorem ILTB, 1180
injective linear transformations
    dimension
        theorem ILTD, 1181
inner product
    anti-commutative
        theorem IPAC, 1182
    example CSIP, 1183
    norm
        theorem IPN, 1184
    notation, 1185
    positive
        theorem PIP, 1186
    scalar multiplication
        theorem IPSM, 1187
    vector addition
        theorem IPVA, 1188
integers
    mod p
        definition IMP, 1189
    mod p, field
        theorem FIMP, 1190
    mod 11
        example IM11, 1191
interpolating polynomial
    theorem IP, 1192
invariant subspace
    definition IS, 1193
    eigenspace, 1194
    eigenspaces
        example EIS, 1195
    example TIS, 1196
    Jordan block
        example ISJB, 1197
    kernels of powers
        theorem KPIS, 1198
inverse
    composition of linear transformations
        theorem ICLT, 1199
    example CMI, 1200
    example MI, 1201
    notation, 1202
    of a matrix, 1203
invertible linear transformation
    defined by invertible matrix
        theorem IMILT, 1204
invertible linear transformations
    composition
        theorem CIVLT, 1205
IP (definition), 1206
IP (notation), 1207
IP (subsection, section O), 1208
IP (theorem), 1209
IPAC (theorem), 1210
IPN (theorem), 1211
IPSM (theorem), 1212
IPVA (theorem), 1213
IS (definition), 1214
IS (example), 1215
IS (section), 1216
IS (subsection, section IS), 1217
ISJB (example), 1218
ISMR4 (example), 1219
ISMR6 (example), 1220
isomorphic
    multiple vector spaces
        example MIVS, 1221
    vector spaces
        example IVSAV, 1222
isomorphic vector spaces
    dimension
        theorem IVSED, 1223
    example TIVS, 1224
ISRN (theorem), 1225
ISSI (example), 1226
ITMT (theorem), 1227
IV (subsection, section IVLT), 1228
IVLT (definition), 1229
IVLT (section), 1230
IVLT (subsection, section IVLT), 1231
IVLT (subsection, section MR), 1232
IVS (definition), 1233
IVSAV (example), 1234
IVSED (theorem), 1235

J (archetype), 1236
JB (definition), 1237
JB (notation), 1238
JB4 (example), 1239
JCF (definition), 1240
JCF (section), 1241
JCF (subsection, section JCF), 1242
JCF10 (example), 1243
JCFLT (theorem), 1244
Jordan block
    definition JB, 1245
    nilpotent
        theorem NJB, 1246
    notation, 1247
    size 4
        example JB4, 1248
Jordan canonical form
    definition JCF, 1249
    size 10
        example JCF10, 1250

K (archetype), 1251
kernel
    injective linear transformation
        theorem KILT, 1252
    isomorphic to null space
        theorem KNSI, 1253
    linear transformation
        example NKAO, 1254
    notation, 1255
    of a linear transformation
        definition KLT, 1256
    pre-image, 1257
    subspace
        theorem KLTS, 1258
    trivial
        example TKAP, 1259
    via matrix representation
        example KVMR, 1260
KILT (theorem), 1261
KLT (definition), 1262
KLT (notation), 1263
KLT (subsection, section ILT), 1264
KLTS (theorem), 1265
KNSI (theorem), 1266
KPI (theorem), 1267
KPIS (theorem), 1268
KPLT (theorem), 1269
KPNLT (example), 1270
KPNLT (theorem), 1271
KVMR (example), 1272

L (archetype), 1273
L (technique, section PT), 1274
LA (subsection, section WILA), 1275
LC (definition), 1276
LC (section), 1277
LC (subsection, section LC), 1278
LC (technique, section PT), 1279
LCCV (definition), 1280
LCM (example), 1281
LDCAA (example), 1282
LDHS (example), 1283
LDP4 (example), 1284
LDRN (example), 1285
LDS (example), 1286
LDS (section), 1287
LDSS (subsection, section LDS), 1288
least squares
    minimizes residuals
        theorem LSMR, 1289
least squares solution
    definition LSS, 1290
left null space
    as row space, 1291
    definition LNS, 1292
    example LNS, 1293
    notation, 1294
    subspace
        theorem LNSMS, 1295
lemma
    technique LC, 1296
LI (definition), 1297
LI (section), 1298
LI (subsection, section LISS), 1299
LIC (example), 1300
LICAB (example), 1301
LICV (definition), 1302
LIHS (example), 1303
LIM32 (example), 1304
linear combination
    system of equations
        example ABLC, 1305
    definition LC, 1306
    definition LCCV, 1307
    example TLC, 1308
    linear transformation, 1309
    matrices
        example LCM, 1310
    system of equations
        example AALC, 1311
linear combinations
    solutions to linear systems
        theorem SLSLC, 1312
linear dependence
    more vectors than size
        theorem MVSLD, 1313
linear independence
    definition LI, 1314
    definition LICV, 1315
    homogeneous systems
        theorem LIVHS, 1316
    injective linear transformation
        theorem ILTLI, 1317
    matrices
        example LIM32, 1318
    orthogonal, 1319
    r and n
        theorem LIVRN, 1320
linear solve
    mathematica, 1321
linear system
    consistent
        theorem RCLS, 1322
    matrix representation
        definition LSMR, 1323
        notation, 1324
linear systems
    notation
        example MNSLE, 1325
        example NSLE, 1326
linear transformation
    polynomials to polynomials
        example LTPP, 1327
    addition
        definition LTA, 1328
        theorem MLTLT, 1329
        theorem SLTLT, 1330
    as matrix multiplication
        example ALTMM, 1331
    basis of range
        example BRLT, 1332
    checking
        example ALT, 1333
    composition
        definition LTC, 1334
        theorem CLTLT, 1335
    defined by a matrix
        example LTM, 1336
    defined on a basis
        example LTDB1, 1337
        example LTDB2, 1338
        example LTDB3, 1339
        theorem LTDB, 1340
    definition LT, 1341
    identity
        definition IDLT, 1342
    injection
        definition ILT, 1343
    inverse
        theorem ILTLT, 1344
    inverse of inverse
        theorem IILT, 1345
    invertible
        definition IVLT, 1346
        example AIVLT, 1347
    invertible, injective and surjective
        theorem ILTIS, 1348
    Jordan canonical form
        theorem JCFLT, 1349
    kernels of powers
        theorem KPLT, 1350
    linear combination
        theorem LTLC, 1351
    matrix of, 1352
        example MFLT, 1353
        example MOLT, 1354
    not
        example NLT, 1355
    not invertible
        example ANILT, 1356
    notation, 1357
    polynomials to matrices
        example LTPM, 1358
    rank plus nullity
        theorem RPNDD, 1359
    restriction
        definition LTR, 1360
        notation, 1361
    scalar multiple
        example SMLT, 1362
    scalar multiplication
        definition LTSM, 1363
    spanning range
        theorem SSRLT, 1364
    sum
        example STLT, 1365
    surjection
        definition SLT, 1366
    vector space of, 1367
    zero vector
        theorem LTTZZ, 1368
linear transformation inverse
    via matrix representation
        example ILTVR, 1369
linear transformation restriction
    on generalized eigenspace
        example LTRGE, 1370
linear transformations
    compositions
        example CTLT, 1371
    from matrices
        theorem MBLT, 1372
linearly dependent
    r < n
        example LDRN, 1373
    via homogeneous system
        example LDHS, 1374
linearly dependent columns
    Archetype A
        example LDCAA, 1375
linearly dependent set
    example LDS, 1376
    linear combinations within
        theorem DLDS, 1377
    polynomials
        example LDP4, 1378
linearly independent
    crazy vector space
        example LIC, 1379
    extending sets
        theorem ELIS, 1380
    polynomials
        example LIP4, 1381
    via homogeneous system
        example LIHS, 1382
linearly independent columns
    Archetype B
        example LICAB, 1383
linearly independent set
    example LIS, 1384
    example LLDS, 1385
LINM (subsection, section LI), 1386
LINSB (example), 1387
LIP4 (example), 1388
LIS (example), 1389
LISS (section), 1390
LISV (subsection, section LI), 1391
LIVHS (theorem), 1392
LIVRN (theorem), 1393
LLDS (example), 1394
LNS (definition), 1395
LNS (example), 1396
LNS (notation), 1397
LNS (subsection, section FS), 1398
LNSMS (theorem), 1399
lower triangular matrix
    definition LTM, 1400
LS.MMA (computation, section MMA), 1401
LSMR (definition), 1402
LSMR (notation), 1403
LSMR (theorem), 1404
LSS (definition), 1405
LT (chapter), 1406
LT (definition), 1407
LT (notation), 1408
LT (section), 1409
LT (subsection, section LT), 1410
LTA (definition), 1411
LTC (definition), 1412
LTDB (theorem), 1413
LTDB1 (example), 1414
LTDB2 (example), 1415
LTDB3 (example), 1416
LTLC (subsection, section LT), 1417
LTLC (theorem), 1418
LTM (definition), 1419
LTM (example), 1420
LTPM (example), 1421
LTPP (example), 1422
LTR (definition), 1423
LTR (notation), 1424
LTRGE (example), 1425
LTSM (definition), 1426
LTTZZ (theorem), 1427

M (archetype), 1428
M (chapter), 1429
M (definition), 1430
M (notation), 1431
MA (definition), 1432
MA (example), 1433
MA (notation), 1434
MACN (Property), 1435
MAF (Property), 1436
MAP (subsection, section SVD), 1437
mathematica
    gram-schmidt (computation), 1438
    linear solve (computation), 1439
    matrix entry (computation), 1440
    matrix inverse (computation), 1441
    matrix multiplication (computation), 1442
    null space (computation), 1443
    row reduce (computation), 1444
    transpose of a matrix (computation), 1445
    vector form of solutions (computation), 1446
    vector linear combinations (computation), 1447
mathematical language
    technique L, 1448
matrix
    addition
        definition MA, 1449
        notation, 1450
    augmented
        definition AM, 1451
    column space
        definition CSM, 1452
    complex conjugate
        example CCM, 1453
    definition M, 1454
    equality
        definition ME, 1455
        notation, 1456
    example AM, 1457
    identity
        definition IM, 1458
    inverse
        definition MI, 1459
    nonsingular
        definition NM, 1460
    notation, 1461
    of a linear transformation
        theorem MLTCV, 1462
    product
        example PTM, 1463
        example PTMEE, 1464
    product with vector
        definition MVP, 1465
    rectangular, 1466
    row space
        definition RSM, 1467
    scalar multiplication
        definition MSM, 1468
        notation, 1469
    singular, 1470
    square
        definition SQM, 1471
    submatrices
        example SS, 1472
    submatrix
        definition SM, 1473
    symmetric
        definition SYM, 1474
    transpose
        definition TM, 1475
    unitary
        definition UM, 1476
    unitary is invertible
        theorem UMI, 1477
    zero
        definition ZM, 1478
matrix addition
    example MA, 1479
matrix components
    notation, 1480
matrix entry
    mathematica, 1481
    ti83, 1482
    ti86, 1483
matrix inverse
    Archetype B, 1484
    computation
        theorem CINM, 1485
    mathematica, 1486
    nonsingular matrix
        theorem NI, 1487
    of a matrix inverse
        theorem MIMI, 1488
    one-sided
        theorem OSIS, 1489
    product
        theorem SS, 1490
    scalar multiple
        theorem MISM, 1491
    size 2 matrices
        theorem TTMI, 1492
    transpose
        theorem MIT, 1493
    uniqueness
        theorem MIU, 1494
matrix multiplication
    adjoints
        theorem MMAD, 1495
    associativity
        theorem MMA, 1496
    complex conjugation
        theorem MMCC, 1497
    definition MM, 1498
    distributivity
        theorem MMDAA, 1499
    entry-by-entry
        theorem EMP, 1500
    identity matrix
        theorem MMIM, 1501
    inner product
        theorem MMIP, 1502
    mathematica, 1503
    noncommutative
        example MMNC, 1504
    scalar matrix multiplication
        theorem MMSMM, 1505
    systems of linear equations
        theorem SLEMM, 1506
    transposes
        theorem MMT, 1507
    zero matrix
        theorem MMZM, 1508
matrix product
    as composition of linear transformations
        example MPMR, 1509
matrix representation
    basis of eigenvectors
        example MRBE, 1510
    composition of linear transformations
        theorem MRCLT, 1511
    definition MR, 1512
    invertible
        theorem IMR, 1513
    multiple of a linear transformation
        theorem MRMLT, 1514
    restriction to generalized eigenspace
        theorem MRRGE, 1515
    sum of linear transformations
        theorem MRSLT, 1516
    theorem FTMR, 1517
    upper triangular
        theorem UTMR, 1518
matrix representations
    converting with change-of-basis
        example MRCM, 1519
    example OLTTR, 1520
matrix scalar multiplication
    example MSM, 1521
matrix vector space
    dimension
        theorem DM, 1522
matrix-adjoint product
    eigenvalues, eigenvectors
        theorem EEMAP, 1523
matrix-vector product
    example MTV, 1524
    notation, 1525
MBC (example), 1526
MBLT (theorem), 1527
MC (notation), 1528
MCC (subsection, section MO), 1529
MCCN (Property), 1530
MCF (Property), 1531, 1532
MCN (definition), 1533
MCN (subsection, section CNO), 1534
MCSM (example), 1535
MCT (theorem), 1536
MD (chapter), 1537
ME (definition), 1538
ME (notation), 1539
ME (subsection, section PEE), 1540
ME (technique, section PT), 1541
ME (theorem), 1542
ME.MMA (computation, section MMA), 1543
ME.TI83 (computation, section TI83), 1544
ME.TI86 (computation, section TI86), 1545
MEASM (subsection, section MO), 1546
MFLT (example), 1547
MI (definition), 1548
MI (example), 1549
MI (notation), 1550
MI.MMA (computation, section MMA), 1551
MICN (Property), 1552
MIF (Property), 1553
MIMI (theorem), 1554
MINM (section), 1555
MISLE (section), 1556
MISM (theorem), 1557
MIT (theorem), 1558
MIU (theorem), 1559
MIVS (example), 1560
MLT (subsection, section LT), 1561
MLTCV (theorem), 1562
MLTLT (theorem), 1563
MM (definition), 1564
MM (section), 1565
MM (subsection, section MM), 1566
MM.MMA (computation, section MMA), 1567
MMA (section), 1568
MMA (theorem), 1569
MMAD (theorem), 1570
MMCC (theorem), 1571
MMDAA (theorem), 1572
MMEE (subsection, section MM), 1573
MMIM (theorem), 1574
MMIP (theorem), 1575
MMNC (example), 1576
MMSMM (theorem), 1577
MMT (theorem), 1578
MMZM (theorem), 1579
MNEM (theorem), 1580
MNSLE (example), 1581
MO (section), 1582
MOLT (example), 1583
more variables than equations
    example OSGMD, 1584
    theorem CMVEI, 1585
MPMR (example), 1586
MR (definition), 1587
MR (section), 1588
MRBE (example), 1589
MRCB (theorem), 1590
MRCLT (theorem), 1591
MRCM (example), 1592
MRMLT (theorem), 1593
MRRGE (theorem), 1594
MRS (subsection, section CB), 1595
MRSLT (theorem), 1596
MSCN (example), 1597
MSM (definition), 1598
MSM (example), 1599
MSM (notation), 1600
MTV (example), 1601
multiplicative associativity
    complex numbers
        Property MACN, 1602
multiplicative closure
    field
        Property MCF, 1603
multiplicative commuativity
    complex numbers
        Property MCCN, 1604
multiplicative inverse
    complex numbers
        Property MICN, 1605
MVNSE (subsection, section RREF), 1606
MVP (definition), 1607
MVP (notation), 1608
MVP (subsection, section MM), 1609
MVSLD (theorem), 1610
MWIAA (example), 1611

N (archetype), 1612
N (subsection, section O), 1613
N (technique, section PT), 1614
NDMS4 (example), 1615
negation of statements
    technique N, 1616
NEM (theorem), 1617
NI (theorem), 1618
NIAO (example), 1619
NIAQ (example), 1620
NIAQR (example), 1621
NIDAU (example), 1622
nilpotent
    linear transformation
        definition NLT, 1623
NJB (theorem), 1624
NJB5 (example), 1625
NKAO (example), 1626
NLT (definition), 1627
NLT (example), 1628
NLT (section), 1629
NLT (subsection, section NLT), 1630
NLTFO (subsection, section LT), 1631
NM (definition), 1632
NM (example), 1633
NM (section), 1634
NM (subsection, section NM), 1635
NM (subsection, section OD), 1636
NM62 (example), 1637
NM64 (example), 1638
NM83 (example), 1639
NME1 (theorem), 1640
NME2 (theorem), 1641
NME3 (theorem), 1642
NME4 (theorem), 1643
NME5 (theorem), 1644
NME6 (theorem), 1645
NME7 (theorem), 1646
NME8 (theorem), 1647
NME9 (theorem), 1648
NMI (subsection, section MINM), 1649
NMLIC (theorem), 1650
NMPEM (theorem), 1651
NMRRI (theorem), 1652
NMTNS (theorem), 1653
NMUS (theorem), 1654
NOILT (theorem), 1655
NOLT (definition), 1656
NOLT (notation), 1657
NOM (definition), 1658
NOM (notation), 1659
nonsingular
    columns as basis
        theorem CNMB, 1660
nonsingular matrices
    linearly independent columns
        theorem NMLIC, 1661
nonsingular matrix
    Archetype B
        example NM, 1662
    column space, 1663
    elemntary matrices
        theorem NMPEM, 1664
    equivalences
        theorem NME1, 1665
        theorem NME2, 1666
        theorem NME3, 1667
        theorem NME4, 1668
        theorem NME5, 1669
        theorem NME6, 1670
        theorem NME7, 1671
        theorem NME8, 1672
        theorem NME9, 1673
    matrix inverse, 1674
    null space
        example NSNM, 1675
    nullity, 1676
    product of nonsingular matrices
        theorem NPNT, 1677
    rank
        theorem RNNM, 1678
    row-reduced
        theorem NMRRI, 1679
    trivial null space
        theorem NMTNS, 1680
    unique solutions
        theorem NMUS, 1681
nonsingular matrix, row-reduced
    example NSR, 1682
norm
    example CNSV, 1683
    inner product, 1684
    notation, 1685
normal matrix
    definition NRML, 1686
    example ANM, 1687
    orthonormal basis, 1688
notation
    A, 1689
    AM, 1690
    C, 1691
    CCCV, 1692
    CCM, 1693
    CCN, 1694
    CNA, 1695
    CNE, 1696
    CNM, 1697
    CSM, 1698
    CV, 1699
    CVA, 1700
    CVC, 1701
    CVE, 1702
    CVSM, 1703
    D, 1704
    DM, 1705
    DS, 1706
    ELEM, 1707
    ES, 1708
    GES, 1709
    IE, 1710
    IM, 1711
    IP, 1712
    JB, 1713
    KLT, 1714
    LNS, 1715
    LSMR, 1716
    LT, 1717
    LTR, 1718
    M, 1719
    MA, 1720
    MC, 1721
    ME, 1722
    MI, 1723
    MSM, 1724
    MVP, 1725
    NOLT, 1726
    NOM, 1727
    NSM, 1728
    NV, 1729
    RLT, 1730
    RO, 1731
    ROLT, 1732
    ROM, 1733
    RREFA, 1734
    RSM, 1735
    SC, 1736
    SE, 1737
    SETM, 1738
    SI, 1739
    SM, 1740
    SRM, 1741
    SSET, 1742
    SSV, 1743
    SU, 1744
    T, 1745
    TM, 1746
    VSCV, 1747
    VSM, 1748
    ZCV, 1749
    ZM, 1750
notation for a linear system
    example NSE, 1751
NPNT (theorem), 1752
NRFO (subsection, section MR), 1753
NRML (definition), 1754
NRREF (example), 1755
NS.MMA (computation, section MMA), 1756
NSAO (example), 1757
NSAQ (example), 1758
NSAQR (example), 1759
NSC2A (example), 1760
NSC2S (example), 1761
NSC2Z (example), 1762
NSDAT (example), 1763
NSDS (example), 1764
NSE (example), 1765
NSEAI (example), 1766
NSLE (example), 1767
NSLIL (example), 1768
NSM (definition), 1769
NSM (notation), 1770
NSM (subsection, section HSE), 1771
NSMS (theorem), 1772
NSNM (example), 1773
NSNM (subsection, section NM), 1774
NSR (example), 1775
NSS (example), 1776
NSSLI (subsection, section LI), 1777
Null space
    as a span
        example NSDS, 1778
null space
    Archetype I
        example NSEAI, 1779
    basis
        theorem BNS, 1780
    computation
        example CNS1, 1781
        example CNS2, 1782
    isomorphic to kernel, 1783
    linearly independent basis
        example LINSB, 1784
    mathematica, 1785
    matrix
        definition NSM, 1786
    nonsingular matrix, 1787
    notation, 1788
    singular matrix, 1789
    spanning set
        example SSNS, 1790
        theorem SSNS, 1791
    subspace
        theorem NSMS, 1792
null space span, linearly independent
    Archetype L
        example NSLIL, 1793
nullity
    computing, 1794
    injective linear transformation
        theorem NOILT, 1795
    linear transformation
        definition NOLT, 1796
    matrix, 1797
        definition NOM, 1798
    notation, 1799, 1800
    square matrix, 1801
NV (definition), 1802
NV (notation), 1803
NVM (theorem), 1804

O (archetype), 1805
O (Property), 1806
O (section), 1807
OBC (subsection, section B), 1808
OBNM (theorem), 1809
OBUTR (theorem), 1810
OC (Property), 1811
OCN (Property), 1812
OD (section), 1813
OD (subsection, section OD), 1814
OD (theorem), 1815
OF (Property), 1816
OLTTR (example), 1817
OM (Property), 1818
one
    column vectors
        Property OC, 1819
    complex numbers
        Property OCN, 1820
    field
        Property OF, 1821
    matrices
        Property OM, 1822
    vectors
        Property O, 1823
ONFV (example), 1824
ONS (definition), 1825
ONTV (example), 1826
orthogonal
    linear independence
        theorem OSLI, 1827
    set
        example AOS, 1828
    set of vectors
        definition OSV, 1829
    vector pairs
        definition OV, 1830
orthogonal vectors
    example TOV, 1831
orthonormal
    definition ONS, 1832
    matrix columns
        example OSMC, 1833
orthonormal basis
    normal matrix
        theorem OBNM, 1834
orthonormal diagonalization
    theorem OD, 1835
orthonormal set
    four vectors
        example ONFV, 1836
    three vectors
        example ONTV, 1837
OSGMD (example), 1838
OSIS (theorem), 1839
OSLI (theorem), 1840
OSMC (example), 1841
OSV (definition), 1842
OV (definition), 1843
OV (subsection, section O), 1844

P (appendix), 1845
P (archetype), 1846
P (technique, section PT), 1847
particular solutions
    example PSHS, 1848
PCNA (theorem), 1849
PCVS (example), 1850
PD (section), 1851
PDM (section), 1852
PDM (theorem), 1853
PEE (section), 1854
PEEF (theorem), 1855
PI (definition), 1856
PI (subsection, section LT), 1857
PI (technique, section PT), 1858
PIP (theorem), 1859
PM (example), 1860
PM (subsection, section EE), 1861
PMI (subsection, section MISLE), 1862
PMM (subsection, section MM), 1863
PMR (subsection, section MR), 1864
PNLT (subsection, section NLT), 1865
POD (section), 1866
polar decomposition
    theorem PDM, 1867
polynomial
    of a matrix
        example PM, 1868
polynomial vector space
    dimension
        theorem DP, 1869
positive semi-definite
    creating
        theorem CPSM, 1870
positive semi-definite matrix
    definition PSM, 1871
    eigenvalues
        theorem EPSM, 1872
practice
    technique P, 1873
pre-image
    definition PI, 1874
    kernel
        theorem KPI, 1875
pre-images
    example SPIAS, 1876
principal axis theorem, 1877
product of triangular matrices
    theorem PTMT, 1878
Property
    AA, 1879
    AAC, 1880
    AACN, 1881
    AAF, 1882
    AAM, 1883
    AC, 1884
    ACC, 1885
    ACCN, 1886
    ACF, 1887, 1888
    ACM, 1889
    AI, 1890
    AIC, 1891
    AICN, 1892
    AIF, 1893
    AIM, 1894
    C, 1895
    CC, 1896
    CM, 1897
    DCN, 1898
    DF, 1899
    DMAM, 1900
    DSA, 1901
    DSAC, 1902
    DSAM, 1903
    DVA, 1904
    DVAC, 1905
    MACN, 1906
    MAF, 1907
    MCCN, 1908
    MCF, 1909, 1910
    MICN, 1911
    MIF, 1912
    O, 1913
    OC, 1914
    OCN, 1915
    OF, 1916
    OM, 1917
    SC, 1918
    SCC, 1919
    SCM, 1920
    SMA, 1921
    SMAC, 1922
    SMAM, 1923
    Z, 1924
    ZC, 1925
    ZCN, 1926
    ZF, 1927
    ZM, 1928
PSHS (example), 1929
PSHS (subsection, section LC), 1930
PSM (definition), 1931
PSM (section), 1932
PSM (subsection, section PSM), 1933
PSM (subsection, section SD), 1934
PSMSR (theorem), 1935
PSPHS (theorem), 1936
PSS (subsection, section SSLE), 1937
PSSD (theorem), 1938
PSSLS (theorem), 1939
PT (section), 1940
PTFP (example), 1941
PTM (example), 1942
PTMEE (example), 1943
PTMT (theorem), 1944

Q (archetype), 1945

R (archetype), 1946
R (chapter), 1947
range
    full
        example FRAN, 1948
    isomorphic to column space
        theorem RCSI, 1949
    linear transformation
        example RAO, 1950
    notation, 1951
    of a linear transformation
        definition RLT, 1952
    pre-image
        theorem RPI, 1953
    subspace
        theorem RLTS, 1954
    surjective linear transformation
        theorem RSLT, 1955
    via matrix representation
        example RVMR, 1956
rank
    computing
        theorem CRN, 1957
    linear transformation
        definition ROLT, 1958
    matrix
        definition ROM, 1959
        example RNM, 1960
    notation, 1961, 1962
    of transpose
        example RRTI, 1963
    square matrix
        example RNSM, 1964
    surjective linear transformation
        theorem ROSLT, 1965
    transpose
        theorem RMRT, 1966
rank one decomposition
    size 2
        example ROD2, 1967
    size 4
        example ROD4, 1968
    theorem ROD, 1969
rank+nullity
    theorem RPNC, 1970
RAO (example), 1971
RCLS (theorem), 1972
RCSI (theorem), 1973
RD (subsection, section VS), 1974
RDS (theorem), 1975
READ (subsection, section B), 1976
READ (subsection, section CB), 1977
READ (subsection, section CRS), 1978
READ (subsection, section D), 1979
READ (subsection, section DM), 1980
READ (subsection, section EE), 1981
READ (subsection, section FS), 1982
READ (subsection, section HSE), 1983
READ (subsection, section ILT), 1984
READ (subsection, section IVLT), 1985
READ (subsection, section LC), 1986
READ (subsection, section LDS), 1987
READ (subsection, section LI), 1988
READ (subsection, section LISS), 1989
READ (subsection, section LT), 1990
READ (subsection, section MINM), 1991
READ (subsection, section MISLE), 1992
READ (subsection, section MM), 1993
READ (subsection, section MO), 1994
READ (subsection, section MR), 1995
READ (subsection, section NM), 1996
READ (subsection, section O), 1997
READ (subsection, section PD), 1998
READ (subsection, section PDM), 1999
READ (subsection, section PEE), 2000
READ (subsection, section RREF), 2001
READ (subsection, section S), 2002
READ (subsection, section SD), 2003
READ (subsection, section SLT), 2004
READ (subsection, section SS), 2005
READ (subsection, section SSLE), 2006
READ (subsection, section TSS), 2007
READ (subsection, section VO), 2008
READ (subsection, section VR), 2009
READ (subsection, section VS), 2010
READ (subsection, section WILA), 2011
reduced row-echelon form
    analysis
        notation, 2012
    definition RREF, 2013
    example NRREF, 2014
    example RREF, 2015
    extended
        definition EEF, 2016
    notation
        example RREFN, 2017
    unique
        theorem RREFU, 2018
reducing a span
    example RSC5, 2019
relation of linear dependence
    definition RLD, 2020
    definition RLDCV, 2021
REM (definition), 2022
REMEF (theorem), 2023
REMES (theorem), 2024
REMRS (theorem), 2025
RES (example), 2026
RGEN (theorem), 2027
RLD (definition), 2028
RLDCV (definition), 2029
RLT (definition), 2030
RLT (notation), 2031
RLT (subsection, section IS), 2032
RLT (subsection, section SLT), 2033
RLTS (theorem), 2034
RMRT (theorem), 2035
RNLT (subsection, section IVLT), 2036
RNM (example), 2037
RNM (subsection, section D), 2038
RNNM (subsection, section D), 2039
RNNM (theorem), 2040
RNSM (example), 2041
RO (definition), 2042
RO (notation), 2043
RO (subsection, section RREF), 2044
ROD (section), 2045
ROD (theorem), 2046
ROD2 (example), 2047
ROD4 (example), 2048
ROLT (definition), 2049
ROLT (notation), 2050
ROM (definition), 2051
ROM (notation), 2052
ROSLT (theorem), 2053
row operations
    definition RO, 2054
    elementary matrices, 2055, 2056
    notation, 2057
row reduce
    mathematica, 2058
    ti83, 2059
    ti86, 2060
row space
    Archetype I
        example RSAI, 2061
    as column space, 2062
    basis
        example RSB, 2063
        theorem BRS, 2064
    matrix, 2065
    notation, 2066
    row-equivalent matrices
        theorem REMRS, 2067
    subspace
        theorem RSMS, 2068
row-equivalent matrices
    definition REM, 2069
    example TREM, 2070
    row space, 2071
    row spaces
        example RSREM, 2072
    theorem REMES, 2073
row-reduce
    the verb
        definition RR, 2074
row-reduced matrices
    theorem REMEF, 2075
RPI (theorem), 2076
RPNC (theorem), 2077
RPNDD (theorem), 2078
RR (definition), 2079
RR.MMA (computation, section MMA), 2080
RR.TI83 (computation, section TI83), 2081
RR.TI86 (computation, section TI86), 2082
RREF (definition), 2083
RREF (example), 2084
RREF (section), 2085
RREF (subsection, section RREF), 2086
RREFA (notation), 2087
RREFN (example), 2088
RREFU (theorem), 2089
RRTI (example), 2090
RS (example), 2091
RSAI (example), 2092
RSB (example), 2093
RSC5 (example), 2094
RSLT (theorem), 2095
RSM (definition), 2096
RSM (notation), 2097
RSM (subsection, section CRS), 2098
RSMS (theorem), 2099
RSNS (example), 2100
RSREM (example), 2101
RSSC4 (example), 2102
RT (subsection, section PD), 2103
RVMR (example), 2104

S (archetype), 2105
S (definition), 2106
S (example), 2107
S (section), 2108
SAA (example), 2109
SAB (example), 2110
SABMI (example), 2111
SAE (example), 2112
SAN (example), 2113
SAR (example), 2114
SAS (section), 2115
SAV (example), 2116
SC (definition), 2117
SC (example), 2118
SC (notation), 2119
SC (Property), 2120
SC (subsection, section S), 2121
SC (subsection, section SET), 2122
SC3 (example), 2123
SCAA (example), 2124
SCAB (example), 2125
SCAD (example), 2126
scalar closure
    column vectors
        Property SCC, 2127
    matrices
        Property SCM, 2128
    vectors
        Property SC, 2129
scalar multiple
    matrix inverse, 2130
scalar multiplication
    zero scalar
        theorem ZSSM, 2131
    zero vector
        theorem ZVSM, 2132
    zero vector result
        theorem SMEZV, 2133
scalar multiplication associativity
    column vectors
        Property SMAC, 2134
    matrices
        Property SMAM, 2135
    vectors
        Property SMA, 2136
SCB (theorem), 2137
SCC (Property), 2138
SCM (Property), 2139
SD (section), 2140
SDS (example), 2141
SE (definition), 2142
SE (notation), 2143
secret sharing
    6 ways
        example SS6W, 2144
SEE (example), 2145
SEEF (example), 2146
SER (theorem), 2147
set
    cardinality
        definition C, 2148
        example CS, 2149
        notation, 2150
    complement
        definition SC, 2151
        example SC, 2152
        notation, 2153
    definition SET, 2154
    empty
        definition ES, 2155
    equality
        definition SE, 2156
        notation, 2157
    intersection
        definition SI, 2158
        example SI, 2159
        notation, 2160
    membership
        example SETM, 2161
        notation, 2162
    size, 2163
    subset, 2164
    union
        definition SU, 2165
        example SU, 2166
        notation, 2167
SET (definition), 2168
SET (section), 2169
SETM (example), 2170
SETM (notation), 2171
shoes, 2172
SHS (subsection, section HSE), 2173
SI (definition), 2174
SI (example), 2175
SI (notation), 2176
SI (subsection, section IVLT), 2177
SIM (definition), 2178
similar matrices
    equal eigenvalues
        example EENS, 2179
    eual eigenvalues
        theorem SMEE, 2180
    example SMS3, 2181
    example SMS5, 2182
similarity
    definition SIM, 2183
    equivalence relation
        theorem SER, 2184
singular matrix
    Archetype A
        example S, 2185
    null space
        example NSS, 2186
singular matrix, row-reduced
    example SRR, 2187
singular value decomposition
    theorem SVD, 2188
singular values
    definition SV, 2189
SLE (chapter), 2190
SLE (definition), 2191
SLE (subsection, section SSLE), 2192
SLELT (subsection, section IVLT), 2193
SLEMM (theorem), 2194
SLSLC (theorem), 2195
SLT (definition), 2196
SLT (section), 2197
SLTB (theorem), 2198
SLTD (subsection, section SLT), 2199
SLTD (theorem), 2200
SLTLT (theorem), 2201
SM (definition), 2202
SM (notation), 2203
SM (subsection, section SD), 2204
SM2Z7 (example), 2205
SM32 (example), 2206
SMA (Property), 2207
SMAC (Property), 2208
SMAM (Property), 2209
SMEE (theorem), 2210
SMEZV (theorem), 2211
SMLT (example), 2212
SMS (theorem), 2213
SMS3 (example), 2214
SMS5 (example), 2215
SMZD (theorem), 2216
SMZE (theorem), 2217
SNCM (theorem), 2218
SO (subsection, section SET), 2219
socks, 2220
SOL (subsection, section B), 2221
SOL (subsection, section CB), 2222
SOL (subsection, section CRS), 2223
SOL (subsection, section D), 2224
SOL (subsection, section DM), 2225
SOL (subsection, section EE), 2226
SOL (subsection, section F), 2227
SOL (subsection, section FS), 2228
SOL (subsection, section HSE), 2229
SOL (subsection, section ILT), 2230
SOL (subsection, section IVLT), 2231
SOL (subsection, section LC), 2232
SOL (subsection, section LDS), 2233
SOL (subsection, section LI), 2234
SOL (subsection, section LISS), 2235
SOL (subsection, section LT), 2236
SOL (subsection, section MINM), 2237
SOL (subsection, section MISLE), 2238
SOL (subsection, section MM), 2239
SOL (subsection, section MO), 2240
SOL (subsection, section MR), 2241
SOL (subsection, section NM), 2242
SOL (subsection, section PD), 2243
SOL (subsection, section PDM), 2244
SOL (subsection, section PEE), 2245
SOL (subsection, section RREF), 2246
SOL (subsection, section S), 2247
SOL (subsection, section SD), 2248
SOL (subsection, section SLT), 2249
SOL (subsection, section SS), 2250
SOL (subsection, section SSLE), 2251
SOL (subsection, section T), 2252
SOL (subsection, section TSS), 2253
SOL (subsection, section VO), 2254
SOL (subsection, section VR), 2255
SOL (subsection, section VS), 2256
SOL (subsection, section WILA), 2257
solution set
    Archetype A
        example SAA, 2258
    archetype E
        example SAE, 2259
    theorem PSPHS, 2260
solution sets
    possibilities
        theorem PSSLS, 2261
solution vector
    definition SV, 2262
solving homogeneous system
    Archetype A
        example HISAA, 2263
    Archetype B
        example HUSAB, 2264
    Archetype D
        example HISAD, 2265
solving nonlinear equations
    example STNE, 2266
SP4 (example), 2267
span
    basic
        example ABS, 2268
    basis
        theorem BS, 2269
    definition SS, 2270
    definition SSCV, 2271
    improved
        example IAS, 2272
    notation, 2273
    reducing
        example RSSC4, 2274
    reduction
        example RS, 2275
    removing vectors
        example COV, 2276
    reworking elements
        example RES, 2277
    set of polynomials
        example SSP, 2278
    subspace
        theorem SSS, 2279
span of columns
    Archetype A
        example SCAA, 2280
    Archetype B
        example SCAB, 2281
    Archetype D
        example SCAD, 2282
spanning set
    crazy vector space
        example SSC, 2283
    definition TSVS, 2284
    matrices
        example SSM22, 2285
    more vectors
        theorem SSLD, 2286
    polynomials
        example SSP4, 2287
SPIAS (example), 2288
SQM (definition), 2289
square root
    eigenvalues, eigenspaces
        theorem EESR, 2290
    matrix
        definition SRM, 2291
        notation, 2292
    positive semi-definite matrix
        theorem PSMSR, 2293
    unique
        theorem USR, 2294
SR (section), 2295
SRM (definition), 2296
SRM (notation), 2297
SRM (subsection, section SR), 2298
SRR (example), 2299
SS (definition), 2300
SS (example), 2301
SS (section), 2302
SS (subsection, section LISS), 2303
SS (theorem), 2304
SS6W (example), 2305
SSC (example), 2306
SSCV (definition), 2307
SSET (definition), 2308
SSET (example), 2309
SSET (notation), 2310
SSLD (theorem), 2311
SSLE (section), 2312
SSM22 (example), 2313
SSNS (example), 2314
SSNS (subsection, section SS), 2315
SSNS (theorem), 2316
SSP (example), 2317
SSP4 (example), 2318
SSRLT (theorem), 2319
SSS (theorem), 2320
SSSLT (subsection, section SLT), 2321
SSV (notation), 2322
SSV (subsection, section SS), 2323
starting proofs
    technique GS, 2324
STLT (example), 2325
STNE (example), 2326
SU (definition), 2327
SU (example), 2328
SU (notation), 2329
submatrix
    notation, 2330
subset
    definition SSET, 2331
    notation, 2332
subspace
    as null space
        example RSNS, 2333
    characterized
        example ASC, 2334
    definition S, 2335
    in P4
        example SP4, 2336
    not, additive closure
        example NSC2A, 2337
    not, scalar closure
        example NSC2S, 2338
    not, zero vector
        example NSC2Z, 2339
    testing
        theorem TSS, 2340
    trivial
        definition TS, 2341
    verification
        example SC3, 2342
        example SM32, 2343
subspaces
    equal dimension
        theorem EDYES, 2344
surjective
    Archetype N
        example SAN, 2345
    example SAR, 2346
    not
        example NSAQ, 2347
        example NSAQR, 2348
    not, Archetype O
        example NSAO, 2349
    not, by dimension
        example NSDAT, 2350
    polynomials to matrices
        example SAV, 2351
surjective linear transformation
    bases
        theorem SLTB, 2352
surjective linear transformations
    dimension
        theorem SLTD, 2353
SUV (definition), 2354
SUVB (theorem), 2355
SUVOS (example), 2356
SV (definition), 2357, 2358
SVD (section), 2359
SVD (subsection, section SVD), 2360
SVD (theorem), 2361
SVP4 (example), 2362
SYM (definition), 2363
SYM (example), 2364
symmetric matrices
    theorem SMS, 2365
symmetric matrix
    example SYM, 2366
system of equations
    vector equality
        example VESE, 2367
system of linear equations
    definition SLE, 2368

T (archetype), 2369
T (definition), 2370
T (notation), 2371
T (part), 2372
T (section), 2373
T (technique, section PT), 2374
TCSD (example), 2375
TD (section), 2376
TD (subsection, section TD), 2377
TD (theorem), 2378
TD4 (example), 2379
TDEE (theorem), 2380
TDEE6 (example), 2381
TDSSE (example), 2382
TDSSE (subsection, section TD), 2383
technique
    C, 2384
    CD, 2385
    CP, 2386
    CV, 2387
    D, 2388
    DC, 2389
    E, 2390
    GS, 2391
    I, 2392
    L, 2393
    LC, 2394
    ME, 2395
    N, 2396
    P, 2397
    PI, 2398
    T, 2399
    U, 2400
theorem
    AA, 2401
    AIP, 2402
    AISM, 2403
    AIU, 2404
    AMA, 2405
    AMSM, 2406
    BCS, 2407
    BIS, 2408
    BNS, 2409
    BRS, 2410
    BS, 2411
    CB, 2412
    CBOB, 2413
    CCM, 2414
    CCRA, 2415
    CCRM, 2416
    CCT, 2417
    CFDVS, 2418
    CFNLT, 2419
    CHT, 2420
    CILTI, 2421
    CINM, 2422
    CIVLT, 2423
    CLI, 2424
    CLTLT, 2425
    CMVEI, 2426
    CNMB, 2427
    COB, 2428
    CPSM, 2429
    CRMA, 2430
    CRMSM, 2431
    CRN, 2432
    CRSM, 2433
    CRVA, 2434
    CSCS, 2435
    CSLTS, 2436
    CSMS, 2437
    CSNM, 2438
    CSRN, 2439
    CSRST, 2440
    CSS, 2441
    CUMOS, 2442
    DC, 2443
    DCM, 2444
    DCP, 2445
    DEC, 2446
    DED, 2447
    DEM, 2448
    DEMMM, 2449
    DER, 2450
    DERC, 2451
    DFS, 2452
    DGES, 2453
    DIM, 2454
    DLDS, 2455
    DM, 2456
    DMFE, 2457
    DMST, 2458
    DNLT, 2459
    DP, 2460
    DRCM, 2461
    DRCMA, 2462
    DRCS, 2463
    DRMM, 2464
    DSD, 2465
    DSFB, 2466
    DSFOS, 2467
    DSLI, 2468
    DSZI, 2469
    DSZV, 2470
    DT, 2471
    DVM, 2472
    DZRC, 2473
    EDELI, 2474
    EDYES, 2475
    EEMAP, 2476
    EER, 2477
    EESR, 2478
    EIM, 2479
    EIS, 2480
    ELIS, 2481
    EMDRO, 2482
    EMHE, 2483
    EMMVP, 2484
    EMN, 2485
    EMNS, 2486
    EMP, 2487
    EMRCP, 2488
    EMS, 2489
    ENLT, 2490
    EOMP, 2491
    EOPSS, 2492
    EPM, 2493
    EPSM, 2494
    ERMCP, 2495
    ESMM, 2496
    ETM, 2497
    FIMP, 2498
    FS, 2499
    FTMR, 2500
    FVCS, 2501
    G, 2502
    GEK, 2503
    GESD, 2504
    GESIS, 2505
    GSP, 2506
    HMIP, 2507
    HMOE, 2508
    HMRE, 2509
    HMVEI, 2510
    HSC, 2511
    ICBM, 2512
    ICLT, 2513
    IFDVS, 2514
    IILT, 2515
    ILTB, 2516
    ILTD, 2517
    ILTIS, 2518
    ILTLI, 2519
    ILTLT, 2520
    IMILT, 2521
    IMR, 2522
    IP, 2523
    IPAC, 2524
    IPN, 2525
    IPSM, 2526
    IPVA, 2527
    ISRN, 2528
    ITMT, 2529
    IVSED, 2530
    JCFLT, 2531
    KILT, 2532
    KLTS, 2533
    KNSI, 2534
    KPI, 2535
    KPIS, 2536
    KPLT, 2537
    KPNLT, 2538
    LIVHS, 2539
    LIVRN, 2540
    LNSMS, 2541
    LSMR, 2542
    LTDB, 2543
    LTLC, 2544
    LTTZZ, 2545
    MBLT, 2546
    MCT, 2547
    ME, 2548
    MIMI, 2549
    MISM, 2550
    MIT, 2551
    MIU, 2552
    MLTCV, 2553
    MLTLT, 2554
    MMA, 2555
    MMAD, 2556
    MMCC, 2557
    MMDAA, 2558
    MMIM, 2559
    MMIP, 2560
    MMSMM, 2561
    MMT, 2562
    MMZM, 2563
    MNEM, 2564
    MRCB, 2565
    MRCLT, 2566
    MRMLT, 2567
    MRRGE, 2568
    MRSLT, 2569
    MVSLD, 2570
    NEM, 2571
    NI, 2572
    NJB, 2573
    NME1, 2574
    NME2, 2575
    NME3, 2576
    NME4, 2577
    NME5, 2578
    NME6, 2579
    NME7, 2580
    NME8, 2581
    NME9, 2582
    NMLIC, 2583
    NMPEM, 2584
    NMRRI, 2585
    NMTNS, 2586
    NMUS, 2587
    NOILT, 2588
    NPNT, 2589
    NSMS, 2590
    NVM, 2591
    OBNM, 2592
    OBUTR, 2593
    OD, 2594
    OSIS, 2595
    OSLI, 2596
    PCNA, 2597
    PDM, 2598
    PEEF, 2599
    PIP, 2600
    PSMSR, 2601
    PSPHS, 2602
    PSSD, 2603
    PSSLS, 2604
    PTMT, 2605
    RCLS, 2606
    RCSI, 2607
    RDS, 2608
    REMEF, 2609
    REMES, 2610
    REMRS, 2611
    RGEN, 2612
    RLTS, 2613
    RMRT, 2614
    RNNM, 2615
    ROD, 2616
    ROSLT, 2617
    RPI, 2618
    RPNC, 2619
    RPNDD, 2620
    RREFU, 2621
    RSLT, 2622
    RSMS, 2623
    SCB, 2624
    SER, 2625
    SLEMM, 2626
    SLSLC, 2627
    SLTB, 2628
    SLTD, 2629
    SLTLT, 2630
    SMEE, 2631
    SMEZV, 2632
    SMS, 2633
    SMZD, 2634
    SMZE, 2635
    SNCM, 2636
    SS, 2637
    SSLD, 2638
    SSNS, 2639
    SSRLT, 2640
    SSS, 2641
    SUVB, 2642
    SVD, 2643
    TD, 2644
    TDEE, 2645
    technique T, 2646
    TIST, 2647
    TL, 2648
    TMA, 2649
    TMSM, 2650
    TSE, 2651
    TSRM, 2652
    TSS, 2653
    TT, 2654
    TTMI, 2655
    UMCOB, 2656
    UMI, 2657
    UMPIP, 2658
    USR, 2659
    UTMR, 2660
    VFSLS, 2661
    VRI, 2662
    VRILT, 2663
    VRLT, 2664
    VRRB, 2665
    VRS, 2666
    VSLT, 2667
    VSPCV, 2668
    VSPM, 2669
    ZSSM, 2670
    ZVSM, 2671
    ZVU, 2672
ti83
    matrix entry (computation), 2673
    row reduce (computation), 2674
    vector linear combinations (computation), 2675
TI83 (section), 2676
ti86
    matrix entry (computation), 2677
    row reduce (computation), 2678
    transpose of a matrix (computation), 2679
    vector linear combinations (computation), 2680
TI86 (section), 2681
TIS (example), 2682
TIST (theorem), 2683
TIVS (example), 2684
TKAP (example), 2685
TL (theorem), 2686
TLC (example), 2687
TM (definition), 2688
TM (example), 2689
TM (notation), 2690
TM (subsection, section OD), 2691
TM.MMA (computation, section MMA), 2692
TM.TI86 (computation, section TI86), 2693
TMA (theorem), 2694
TMP (example), 2695
TMSM (theorem), 2696
TOV (example), 2697
trace
    definition T, 2698
    linearity
        theorem TL, 2699
    matrix multiplication
        theorem TSRM, 2700
    notation, 2701
    similarity
        theorem TIST, 2702
    sum of eigenvalues
        theorem TSE, 2703
trail mix
    example TMP, 2704
transpose
    matrix scalar multiplication
        theorem TMSM, 2705
    example TM, 2706
    matrix addition
        theorem TMA, 2707
    matrix inverse, 2708, 2709
    notation, 2710
    scalar multiplication, 2711
transpose of a matrix
    mathematica, 2712
    ti86, 2713
transpose of a transpose
    theorem TT, 2714
TREM (example), 2715
triangular decomposition
    entry by entry, size 6
        example TDEE6, 2716
    entry by entry
        theorem TDEE, 2717
    size 4
        example TD4, 2718
    solving systems of equations
        example TDSSE, 2719
    theorem TD, 2720
triangular matrix
    inverse
        theorem ITMT, 2721
trivial solution
    system of equations
        definition TSHSE, 2722
TS (definition), 2723
TS (subsection, section S), 2724
TSE (theorem), 2725
TSHSE (definition), 2726
TSM (subsection, section MO), 2727
TSRM (theorem), 2728
TSS (section), 2729
TSS (subsection, section S), 2730
TSS (theorem), 2731
TSVS (definition), 2732
TT (theorem), 2733
TTMI (theorem), 2734
TTS (example), 2735
typical systems, 2 × 2
    example TTS, 2736

U (archetype), 2737
U (technique, section PT), 2738
UM (definition), 2739
UM (subsection, section MINM), 2740
UM3 (example), 2741
UMCOB (theorem), 2742
UMI (theorem), 2743
UMPIP (theorem), 2744
unique solution, 3 × 3
    example US, 2745
    example USR, 2746
uniqueness
    technique U, 2747
unit vectors
    basis
        theorem SUVB, 2748
    definition SUV, 2749
    orthogonal
        example SUVOS, 2750
unitary
    permutation matrix
        example UPM, 2751
    size 3
        example UM3, 2752
unitary matrices
    columns
        theorem CUMOS, 2753
unitary matrix
    inner product
        theorem UMPIP, 2754
UPM (example), 2755
upper triangular matrix
    definition UTM, 2756
URREF (subsection, section LC), 2757
US (example), 2758
USR (example), 2759
USR (theorem), 2760
UTM (definition), 2761
UTMR (subsection, section OD), 2762
UTMR (theorem), 2763

V (archetype), 2764
V (chapter), 2765
VA (example), 2766
Vandermonde matrix
    definition VM, 2767
vandermonde matrix
    determinant
        theorem DVM, 2768
    nonsingular
        theorem NVM, 2769
    size 4
        example VM4, 2770
VEASM (subsection, section VO), 2771
vector
    addition
        definition CVA, 2772
    column
        definition CV, 2773
    equality
        definition CVE, 2774
        notation, 2775
    inner product
        definition IP, 2776
    norm
        definition NV, 2777
    notation, 2778
    of constants
        definition VOC, 2779
    product with matrix, 2780, 2781
    scalar multiplication
        definition CVSM, 2782
vector addition
    example VA, 2783
vector component
    notation, 2784
vector form of solutions
    Archetype D
        example VFSAD, 2785
    Archetype I
        example VFSAI, 2786
    Archetype L
        example VFSAL, 2787
    example VFS, 2788
    mathematica, 2789
    theorem VFSLS, 2790
vector linear combinations
    mathematica, 2791
    ti83, 2792
    ti86, 2793
vector representation
    example AVR, 2794
    example VRC4, 2795
    injective
        theorem VRI, 2796
    invertible
        theorem VRILT, 2797
    linear transformation
        definition VR, 2798
        theorem VRLT, 2799
    surjective
        theorem VRS, 2800
    theorem VRRB, 2801
vector representations
    polynomials
        example VRP2, 2802
vector scalar multiplication
    example CVSM, 2803
vector space
    characterization
        theorem CFDVS, 2804
    column vectors
        definition VSCV, 2805
    definition VS, 2806
    infinite dimension
        example VSPUD, 2807
    linear transformations
        theorem VSLT, 2808
    over integers mod 5
        example VSIM5, 2809
vector space of column vectors
    notation, 2810
vector space of functions
    example VSF, 2811
vector space of infinite sequences
    example VSIS, 2812
vector space of matrices
    definition VSM, 2813
    example VSM, 2814
    notation, 2815
vector space of polynomials
    example VSP, 2816
vector space properties
    column vectors
        theorem VSPCV, 2817
    matrices
        theorem VSPM, 2818
vector space, crazy
    example CVS, 2819
vector space, singleton
    example VSS, 2820
vector spaces
    isomorphic
        definition IVS, 2821
        theorem IFDVS, 2822
VESE (example), 2823
VFS (example), 2824
VFSAD (example), 2825
VFSAI (example), 2826
VFSAL (example), 2827
VFSLS (theorem), 2828
VFSS (subsection, section LC), 2829
VFSS.MMA (computation, section MMA), 2830
VLC.MMA (computation, section MMA), 2831
VLC.TI83 (computation, section TI83), 2832
VLC.TI86 (computation, section TI86), 2833
VM (definition), 2834
VM (section), 2835
VM4 (example), 2836
VO (section), 2837
VOC (definition), 2838
VR (definition), 2839
VR (section), 2840
VR (subsection, section LISS), 2841
VRC4 (example), 2842
VRI (theorem), 2843
VRILT (theorem), 2844
VRLT (theorem), 2845
VRP2 (example), 2846
VRRB (theorem), 2847
VRS (theorem), 2848
VS (chapter), 2849
VS (definition), 2850
VS (section), 2851
VS (subsection, section VS), 2852
VSCV (definition), 2853
VSCV (example), 2854
VSCV (notation), 2855
VSF (example), 2856
VSIM5 (example), 2857
VSIS (example), 2858
VSLT (theorem), 2859
VSM (definition), 2860
VSM (example), 2861
VSM (notation), 2862
VSP (example), 2863
VSP (subsection, section MO), 2864
VSP (subsection, section VO), 2865
VSP (subsection, section VS), 2866
VSPCV (theorem), 2867
VSPM (theorem), 2868
VSPUD (example), 2869
VSS (example), 2870

W (archetype), 2871
WILA (section), 2872

X (archetype), 2873

Z (Property), 2874
ZC (Property), 2875
ZCN (Property), 2876
ZCV (definition), 2877
ZCV (notation), 2878
zero
    complex numbers
        Property ZCN, 2879
    field
        Property ZF, 2880
zero column vector
    definition ZCV, 2881
    notation, 2882
zero matrix
    notation, 2883
zero vector
    column vectors
        Property ZC, 2884
    matrices
        Property ZM, 2885
    unique
        theorem ZVU, 2886
    vectors
        Property Z, 2887
ZF (Property), 2888
ZM (definition), 2889
ZM (notation), 2890
ZM (Property), 2891
ZNDAB (example), 2892
ZSSM (theorem), 2893
ZVSM (theorem), 2894
ZVU (theorem), 2895