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
CACN (Property), 136
CAEHW (example), 137
CAF (Property), 138
canonical form
nilpotent linear transformation
example CFNLT, 139
theorem CFNLT, 140
CAV (subsection, section O), 141
Cayley-Hamilton
theorem CHT, 142
CB (section), 143
CB (theorem), 144
CBCV (example), 145
CBM (definition), 146
CBM (subsection, section CB), 147
CBP (example), 148
CC (Property), 149
CCCV (definition), 150
CCCV (notation), 151
CCM (definition), 152
CCM (example), 153
CCM (notation), 154
CCM (theorem), 155
CCN (definition), 156
CCN (notation), 157
CCN (subsection, section CNO), 158
CCRA (theorem), 159
CCRM (theorem), 160
CCT (theorem), 161
CD (subsection, section DM), 162
CD (technique, section PT), 163
CEE (subsection, section EE), 164
CELT (example), 165
CELT (subsection, section CB), 166
CEMS6 (example), 167
CF (section), 168
CFDVS (theorem), 169
CFNLT (example), 170
CFNLT (subsection, section NLT), 171
CFNLT (theorem), 172
CFV (example), 173
change of basis
between polynomials
example CBP, 174
change-of-basis
between column vectors
example CBCV, 175
matrix representation
theorem MRCB, 176
similarity
theorem SCB, 177
theorem CB, 178
change-of-basis matrix
definition CBM, 179
inverse
theorem ICBM, 180
characteristic polynomial
definition CP, 181
degree
theorem DCP, 182
size 3 matrix
example CPMS3, 183
CHT (subsection, section JCF), 184
CHT (theorem), 185
CILT (subsection, section ILT), 186
CILTI (theorem), 187
CIM (subsection, section MISLE), 188
CINM (theorem), 189
CIVLT (example), 190
CIVLT (theorem), 191
CLI (theorem), 192
CLTLT (theorem), 193
CM (definition), 194
CM (Property), 195
CM32 (example), 196
CMCN (Property), 197
CMF (Property), 198
CMI (example), 199
CMIAB (example), 200
CMVEI (theorem), 201
CN (appendix), 202
CNA (definition), 203
CNA (notation), 204
CNA (subsection, section CNO), 205
CNE (definition), 206
CNE (notation), 207
CNM (definition), 208
CNM (notation), 209
CNMB (theorem), 210
CNO (section), 211
CNS1 (example), 212
CNS2 (example), 213
CNSV (example), 214
COB (theorem), 215
coefficient matrix
definition CM, 216
nonsingular
theorem SNCM, 217
column space
as null space
theorem FS, 218
Archetype A
example CSAA, 219
Archetype B
example CSAB, 220
as null space
example CSANS, 221
as null space, Archetype G
example FSAG, 222
as row space
theorem CSRST, 223
basis
theorem BCS, 224
consistent system
theorem CSCS, 225
consistent systems
example CSMCS, 226
isomorphic to range, 227
matrix, 228
nonsingular matrix
theorem CSNM, 229
notation, 230
original columns, Archetype D
example CSOCD, 231
row operations, Archetype I
example CSROI, 232
subspace
theorem CSMS, 233
testing membership
example MCSM, 234
two computations
example CSTW, 235
column vector addition
notation, 236
column vector scalar multiplication
notation, 237
commutativity
column vectors
Property CC, 238
matrices
Property CM, 239
vectors
Property C, 240
complex -space
example VSCV, 241
complex arithmetic
example ACN, 242
complex number
conjugate
example CSCN, 243
modulus
example MSCN, 244
complex number
conjugate
definition CCN, 245
modulus
definition MCN, 246
complex numbers
addition
definition CNA, 247
notation, 248
arithmetic properties
theorem PCNA, 249
equality
definition CNE, 250
notation, 251
multiplication
definition CNM, 252
notation, 253
complex vector space
dimension
theorem DCM, 254
composition
injective linear transformations
theorem CILTI, 255
surjective linear transformations
theorem CSLTS, 256
conjugate
addition
theorem CCRA, 257
column vector
definition CCCV, 258
matrix
definition CCM, 259
notation, 260
multiplication
theorem CCRM, 261
notation, 262
of conjugate of a matrix
theorem CCM, 263
scalar multiplication
theorem CRSM, 264
twice
theorem CCT, 265
vector addition
theorem CRVA, 266
conjugate of a vector
notation, 267
conjugation
matrix addition
theorem CRMA, 268
matrix scalar multiplication
theorem CRMSM, 269
matrix transpose
theorem MCT, 270
consistent linear system, 271
consistent linear systems
theorem CSRN, 272
consistent system
definition CS, 273
constructive proofs
technique C, 274
contradiction
technique CD, 275
contrapositive
technique CP, 276
converse
technique CV, 277
coordinates
orthonormal basis
theorem COB, 278
coordinatization
linear combination of matrices
example CM32, 279
linear independence
theorem CLI, 280
orthonormal basis
example CROB3, 281
example CROB4, 282
spanning sets
theorem CSS, 283
coordinatization principle, 284
coordinatizing
polynomials
example CP2, 285
COV (example), 286
COV (subsection, section LDS), 287
CP (definition), 288
CP (subsection, section VR), 289
CP (technique, section PT), 290
CP2 (example), 291
CPMS3 (example), 292
CPSM (theorem), 293
crazy vector space
example CVSR, 294
properties
example PCVS, 295
CRMA (theorem), 296
CRMSM (theorem), 297
CRN (theorem), 298
CROB3 (example), 299
CROB4 (example), 300
CRS (section), 301
CRS (subsection, section FS), 302
CRSM (theorem), 303
CRVA (theorem), 304
CS (definition), 305
CS (example), 306
CS (subsection, section TSS), 307
CSAA (example), 308
CSAB (example), 309
CSANS (example), 310
CSCN (example), 311
CSCS (theorem), 312
CSIP (example), 313
CSLT (subsection, section SLT), 314
CSLTS (theorem), 315
CSM (definition), 316
CSM (notation), 317
CSMCS (example), 318
CSMS (theorem), 319
CSNM (subsection, section CRS), 320
CSNM (theorem), 321
CSOCD (example), 322
CSRN (theorem), 323
CSROI (example), 324
CSRST (theorem), 325
CSS (theorem), 326
CSSE (subsection, section CRS), 327
CSSOC (subsection, section CRS), 328
CSTW (example), 329
CTD (subsection, section TD), 330
CTLT (example), 331
CUMOS (theorem), 332
curve fitting
polynomial through 5 points
example PTFP, 333
CV (definition), 334
CV (notation), 335
CV (technique, section PT), 336
CVA (definition), 337
CVA (notation), 338
CVC (notation), 339
CVE (definition), 340
CVE (notation), 341
CVS (example), 342
CVS (subsection, section VR), 343
CVSM (definition), 344
CVSM (example), 345
CVSM (notation), 346
CVSR (example), 347
D (acronyms, section PDM), 348
D (archetype), 349
D (chapter), 350
D (definition), 351
D (notation), 352
D (section), 353
D (subsection, section D), 354
D (subsection, section SD), 355
D (technique, section PT), 356
D33M (example), 357
DAB (example), 358
DC (example), 359
DC (technique, section PT), 360
DC (theorem), 361
DCM (theorem), 362
DCN (Property), 363
DCP (theorem), 364
DD (subsection, section DM), 365
DEC (theorem), 366
decomposition
technique DC, 367
DED (theorem), 368
definition
A, 369
AM, 370
AME, 371
B, 372
C, 373
CBM, 374
CCCV, 375
CCM, 376
CCN, 377
CM, 378
CNA, 379
CNE, 380
CNM, 381
CP, 382
CS, 383
CSM, 384
CV, 385
CVA, 386
CVE, 387
CVSM, 388
D, 389
DIM, 390
DM, 391
DS, 392
DZM, 393
EEF, 394
EELT, 395
EEM, 396
ELEM, 397
EM, 398
EO, 399
ES, 400
ESYS, 401
F, 402
GES, 403
GEV, 404
GME, 405
HI, 406
HID, 407
HM, 408
HP, 409
HS, 410
IDLT, 411
IDV, 412
IE, 413
ILT, 414
IM, 415
IMP, 416
IP, 417
IS, 418
IVLT, 419
IVS, 420
JB, 421
JCF, 422
KLT, 423
LC, 424
LCCV, 425
LI, 426
LICV, 427
LNS, 428
LSMR, 429
LSS, 430
LT, 431
LTA, 432
LTC, 433
LTM, 434
LTR, 435
LTSM, 436
M, 437
MA, 438
MCN, 439
ME, 440
MI, 441
MM, 442
MR, 443
MSM, 444
MVP, 445
NLT, 446
NM, 447
NOLT, 448
NOM, 449
NRML, 450
NSM, 451
NV, 452
ONS, 453
OSV, 454
OV, 455
PI, 456
PSM, 457
REM, 458
RLD, 459
RLDCV, 460
RLT, 461
RO, 462
ROLT, 463
ROM, 464
RR, 465
RREF, 466
RSM, 467
S, 468
SC, 469
SE, 470
SET, 471
SI, 472
SIM, 473
SLE, 474
SLT, 475
SM, 476
SOLV, 477
SQM, 478
SRM, 479
SS, 480
SSCV, 481
SSET, 482
SU, 483
SUV, 484
SV, 485
SYM, 486
T, 487
technique D, 488
TM, 489
TS, 490
TSHSE, 491
TSVS, 492
UM, 493
UTM, 494
VM, 495
VOC, 496
VR, 497
VS, 498
VSCV, 499
VSM, 500
ZCV, 501
ZM, 502
DEHD (example), 503
DEM (theorem), 504
DEMMM (theorem), 505
DEMS5 (example), 506
DER (theorem), 507
DERC (theorem), 508
determinant
computed two ways
example TCSD, 509
definition DM, 510
equal rows or columns
theorem DERC, 511
expansion, columns
theorem DEC, 512
expansion, rows
theorem DER, 513
identity matrix
theorem DIM, 514
matrix multiplication
theorem DRMM, 515
nonsingular matrix, 516
notation, 517
row or column multiple
theorem DRCM, 518
row or column swap
theorem DRCS, 519
size 2 matrix
theorem DMST, 520
size 3 matrix
example D33M, 521
transpose
theorem DT, 522
via row operations
example DRO, 523
zero
theorem SMZD, 524
zero row or column
theorem DZRC, 525
zero versus nonzero
example ZNDAB, 526
determinant, upper triangular matrix
example DUTM, 527
determinants
elementary matrices
theorem DEMMM, 528
DF (Property), 529
DF (subsection, section CF), 530
DFS (subsection, section PD), 531
DFS (theorem), 532
DGES (theorem), 533
diagonal matrix
definition DIM, 534
diagonalizable
definition DZM, 535
distinct eigenvalues
example DEHD, 536
theorem DED, 537
full eigenspaces
theorem DMFE, 538
not
example NDMS4, 539
diagonalizable matrix
high power
example HPDM, 540
diagonalization
Archetype B
example DAB, 541
criteria
theorem DC, 542
example DMS3, 543
DIM (definition), 544
DIM (theorem), 545
dimension
crazy vector space
example DC, 546
definition D, 547
notation, 548
polynomial subspace
example DSP4, 549
proper subspaces
theorem PSSD, 550
subspace
example DSM22, 551
direct sum
decomposing zero vector
theorem DSZV, 552
definition DS, 553
dimension
theorem DSD, 554
example SDS, 555
from a basis
theorem DSFB, 556
from one subspace
theorem DSFOS, 557
notation, 558
zero intersection
theorem DSZI, 559
direct sums
linear independence
theorem DSLI, 560
repeated
theorem RDS, 561
distributivity
complex numbers
Property DCN, 562
field
Property DF, 563
distributivity, matrix addition
matrices
Property DMAM, 564
distributivity, scalar addition
column vectors
Property DSAC, 565
matrices
Property DSAM, 566
vectors
Property DSA, 567
distributivity, vector addition
column vectors
Property DVAC, 568
vectors
Property DVA, 569
DLDS (theorem), 570
DLTA (figure), 571
DLTM (figure), 572
DM (definition), 573
DM (notation), 574
DM (section), 575
DM (theorem), 576
DMAM (Property), 577
DMFE (theorem), 578
DMHP (subsection, section HP), 579
DMHP (theorem), 580
DMMP (theorem), 581
DMS3 (example), 582
DMST (theorem), 583
DNLT (theorem), 584
DNMMM (subsection, section PDM), 585
DP (theorem), 586
DRCM (theorem), 587
DRCMA (theorem), 588
DRCS (theorem), 589
DRMM (theorem), 590
DRO (example), 591
DRO (subsection, section PDM), 592
DROEM (subsection, section PDM), 593
DS (definition), 594
DS (notation), 595
DS (subsection, section PD), 596
DSA (Property), 597
DSAC (Property), 598
DSAM (Property), 599
DSD (theorem), 600
DSFB (theorem), 601
DSFOS (theorem), 602
DSLI (theorem), 603
DSM22 (example), 604
DSP4 (example), 605
DSZI (theorem), 606
DSZV (theorem), 607
DT (theorem), 608
DTSLS (figure), 609
DUTM (example), 610
DVA (Property), 611
DVAC (Property), 612
DVM (theorem), 613
DVS (subsection, section D), 614
DZM (definition), 615
DZRC (theorem), 616
E (acronyms, section SD), 617
E (archetype), 618
E (chapter), 619
E (technique, section PT), 620
ECEE (subsection, section EE), 621
EDELI (theorem), 622
EDYES (theorem), 623
EE (section), 624
EEE (subsection, section EE), 625
EEF (definition), 626
EEF (subsection, section FS), 627
EELT (definition), 628
EELT (subsection, section CB), 629
EEM (definition), 630
EEM (subsection, section EE), 631
EEMAP (theorem), 632
EENS (example), 633
EER (theorem), 634
EESR (theorem), 635
EHM (subsection, section PEE), 636
eigenspace
as null space
theorem EMNS, 637
definition EM, 638
invariant subspace
theorem EIS, 639
subspace
theorem EMS, 640
eigenvalue
algebraic multiplicity
definition AME, 641
complex
example CEMS6, 642
definition EEM, 643
existence
example CAEHW, 644
theorem EMHE, 645
geometric multiplicity
definition GME, 646
index, 647
linear transformation
definition EELT, 648
multiplicities
example EMMS4, 649
power
theorem EOMP, 650
root of characteristic polynomial
theorem EMRCP, 651
scalar multiple
theorem ESMM, 652
symmetric matrix
example ESMS4, 653
zero
theorem SMZE, 654
eigenvalues
building desired
example BDE, 655
complex, of a linear transformation
example CELT, 656
conjugate pairs
theorem ERMCP, 657
distinct
example DEMS5, 658
example SEE, 659
Hermitian matrices
theorem HMRE, 660
inverse
theorem EIM, 661
maximum number
theorem MNEM, 662
multiplicities
example HMEM5, 663
theorem ME, 664
number
theorem NEM, 665
of a polynomial
theorem EPM, 666
size 3 matrix
example EMS3, 667
example ESMS3, 668
transpose
theorem ETM, 669
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 670
eigenvector, 671
linear transformation, 672
eigenvectors, 673
conjugate pairs, 674
Hermitian matrices
theorem HMOE, 675
linear transformation
example ELTBM, 676
example ELTBP, 677
linearly independent
theorem EDELI, 678
of a linear transformation
example ELTT, 679
EILT (subsection, section ILT), 680
EIM (theorem), 681
EIS (example), 682
EIS (theorem), 683
ELEM (definition), 684
ELEM (notation), 685
elementary matrices
definition ELEM, 686
determinants
theorem DEM, 687
nonsingular
theorem EMN, 688
notation, 689
row operations
example EMRO, 690
theorem EMDRO, 691
ELIS (theorem), 692
ELTBM (example), 693
ELTBP (example), 694
ELTT (example), 695
EM (definition), 696
EM (subsection, section DM), 697
EMDRO (theorem), 698
EMHE (theorem), 699
EMMS4 (example), 700
EMMVP (theorem), 701
EMN (theorem), 702
EMNS (theorem), 703
EMP (theorem), 704
empty set, 705
notation, 706
EMRCP (theorem), 707
EMRO (example), 708
EMS (theorem), 709
EMS3 (example), 710
ENLT (theorem), 711
EO (definition), 712
EOMP (theorem), 713
EOPSS (theorem), 714
EPM (theorem), 715
EPSM (theorem), 716
equal matrices
via equal matrix-vector products
theorem EMMVP, 717
equation operations
definition EO, 718
theorem EOPSS, 719
equivalence statements
technique E, 720
equivalences
technique ME, 721
equivalent systems
definition ESYS, 722
ERMCP (theorem), 723
ES (definition), 724
ES (notation), 725
ESEO (subsection, section SSLE), 726
ESLT (subsection, section SLT), 727
ESMM (theorem), 728
ESMS3 (example), 729
ESMS4 (example), 730
ESYS (definition), 731
ETM (theorem), 732
EVS (subsection, section VS), 733
example
AALC, 734
ABLC, 735
ABS, 736
ACN, 737
AHSAC, 738
AIVLT, 739
ALT, 740
ALTMM, 741
AM, 742
AMAA, 743
ANILT, 744
ANM, 745
AOS, 746
ASC, 747
AVR, 748
BC, 749
BDE, 750
BDM22, 751
BM, 752
BP, 753
BPR, 754
BRLT, 755
BSM22, 756
BSP4, 757
CABAK, 758
CAEHW, 759
CBCV, 760
CBP, 761
CCM, 762
CELT, 763
CEMS6, 764
CFNLT, 765
CFV, 766
CIVLT, 767
CM32, 768
CMI, 769
CMIAB, 770
CNS1, 771
CNS2, 772
CNSV, 773
COV, 774
CP2, 775
CPMS3, 776
CROB3, 777
CROB4, 778
CS, 779
CSAA, 780
CSAB, 781
CSANS, 782
CSCN, 783
CSIP, 784
CSMCS, 785
CSOCD, 786
CSROI, 787
CSTW, 788
CTLT, 789
CVS, 790
CVSM, 791
CVSR, 792
D33M, 793
DAB, 794
DC, 795
DEHD, 796
DEMS5, 797
DMS3, 798
DRO, 799
DSM22, 800
DSP4, 801
DUTM, 802
EENS, 803
EIS, 804
ELTBM, 805
ELTBP, 806
ELTT, 807
EMMS4, 808
EMRO, 809
EMS3, 810
ESMS3, 811
ESMS4, 812
FDV, 813
FF8, 814
FRAN, 815
FS1, 816
FS2, 817
FSAG, 818
FSCF, 819
GE4, 820
GE6, 821
GENR6, 822
GSTV, 823
HISAA, 824
HISAD, 825
HMEM5, 826
HP, 827
HPDM, 828
HUSAB, 829
IAP, 830
IAR, 831
IAS, 832
IAV, 833
ILTVR, 834
IM, 835
IM11, 836
IS, 837
ISJB, 838
ISMR4, 839
ISMR6, 840
ISSI, 841
IVSAV, 842
JB4, 843
JCF10, 844
KPNLT, 845
KVMR, 846
LCM, 847
LDCAA, 848
LDHS, 849
LDP4, 850
LDRN, 851
LDS, 852
LIC, 853
LICAB, 854
LIHS, 855
LIM32, 856
LINSB, 857
LIP4, 858
LIS, 859
LLDS, 860
LNS, 861
LTDB1, 862
LTDB2, 863
LTDB3, 864
LTM, 865
LTPM, 866
LTPP, 867
LTRGE, 868
MA, 869
MBC, 870
MCSM, 871
MFLT, 872
MI, 873
MIVS, 874
MMNC, 875
MNSLE, 876
MOLT, 877
MPMR, 878
MRBE, 879
MRCM, 880
MSCN, 881
MSM, 882
MTV, 883
MWIAA, 884
NDMS4, 885
NIAO, 886
NIAQ, 887
NIAQR, 888
NIDAU, 889
NJB5, 890
NKAO, 891
NLT, 892
NM, 893
NM62, 894
NM64, 895
NM83, 896
NRREF, 897
NSAO, 898
NSAQ, 899
NSAQR, 900
NSC2A, 901
NSC2S, 902
NSC2Z, 903
NSDAT, 904
NSDS, 905
NSE, 906
NSEAI, 907
NSLE, 908
NSLIL, 909
NSNM, 910
NSR, 911
NSS, 912
OLTTR, 913
ONFV, 914
ONTV, 915
OSGMD, 916
OSMC, 917
PCVS, 918
PM, 919
PSHS, 920
PTFP, 921
PTM, 922
PTMEE, 923
RAO, 924
RES, 925
RNM, 926
RNSM, 927
ROD2, 928
ROD4, 929
RREF, 930
RREFN, 931
RRTI, 932
RS, 933
RSAI, 934
RSB, 935
RSC5, 936
RSNS, 937
RSREM, 938
RSSC4, 939
RVMR, 940
S, 941
SAA, 942
SAB, 943
SABMI, 944
SAE, 945
SAN, 946
SAR, 947
SAV, 948
SC, 949
SC3, 950
SCAA, 951
SCAB, 952
SCAD, 953
SDS, 954
SEE, 955
SEEF, 956
SETM, 957
SI, 958
SM2Z7, 959
SM32, 960
SMLT, 961
SMS3, 962
SMS5, 963
SP4, 964
SPIAS, 965
SRR, 966
SS, 967
SS6W, 968
SSC, 969
SSET, 970
SSM22, 971
SSNS, 972
SSP, 973
SSP4, 974
STLT, 975
STNE, 976
SU, 977
SUVOS, 978
SVP4, 979
SYM, 980
TCSD, 981
TD4, 982
TDEE6, 983
TDSSE, 984
TIS, 985
TIVS, 986
TKAP, 987
TLC, 988
TM, 989
TMP, 990
TOV, 991
TREM, 992
TTS, 993
UM3, 994
UPM, 995
US, 996
USR, 997
VA, 998
VESE, 999
VFS, 1000
VFSAD, 1001
VFSAI, 1002
VFSAL, 1003
VM4, 1004
VRC4, 1005
VRP2, 1006
VSCV, 1007
VSF, 1008
VSIM5, 1009
VSIS, 1010
VSM, 1011
VSP, 1012
VSPUD, 1013
VSS, 1014
ZNDAB, 1015
EXC (subsection, section B), 1016
EXC (subsection, section CB), 1017
EXC (subsection, section CF), 1018
EXC (subsection, section CRS), 1019
EXC (subsection, section D), 1020
EXC (subsection, section DM), 1021
EXC (subsection, section EE), 1022
EXC (subsection, section F), 1023
EXC (subsection, section FS), 1024
EXC (subsection, section HP), 1025
EXC (subsection, section HSE), 1026
EXC (subsection, section ILT), 1027
EXC (subsection, section IVLT), 1028
EXC (subsection, section LC), 1029
EXC (subsection, section LDS), 1030
EXC (subsection, section LI), 1031
EXC (subsection, section LISS), 1032
EXC (subsection, section LT), 1033
EXC (subsection, section MINM), 1034
EXC (subsection, section MISLE), 1035
EXC (subsection, section MM), 1036
EXC (subsection, section MO), 1037
EXC (subsection, section MR), 1038
EXC (subsection, section NM), 1039
EXC (subsection, section O), 1040
EXC (subsection, section PD), 1041
EXC (subsection, section PDM), 1042
EXC (subsection, section PEE), 1043
EXC (subsection, section PSM), 1044
EXC (subsection, section RREF), 1045
EXC (subsection, section S), 1046
EXC (subsection, section SD), 1047
EXC (subsection, section SLT), 1048
EXC (subsection, section SS), 1049
EXC (subsection, section SSLE), 1050
EXC (subsection, section T), 1051
EXC (subsection, section TSS), 1052
EXC (subsection, section VO), 1053
EXC (subsection, section VR), 1054
EXC (subsection, section VS), 1055
EXC (subsection, section WILA), 1056
extended echelon form
submatrices
example SEEF, 1057
extended reduced row-echelon form
properties
theorem PEEF, 1058
F (archetype), 1059
F (definition), 1060
F (section), 1061
F (subsection, section F), 1062
FDV (example), 1063
FF (subsection, section F), 1064
FF8 (example), 1065
Fibonacci sequence
example FSCF, 1066
field
definition F, 1067
figure
DLTA, 1068
DLTM, 1069
DTSLS, 1070
FTMR, 1071
FTMRA, 1072
GLT, 1073
ILT, 1074
MRCLT, 1075
NILT, 1076
FIMP (theorem), 1077
finite field
size 8
example FF8, 1078
four subsets
example FS1, 1079
example FS2, 1080
four subspaces
dimension
theorem DFS, 1081
FRAN (example), 1082
free variables
example CFV, 1083
free variables, number
theorem FVCS, 1084
free, independent variables
example FDV, 1085
FS (section), 1086
FS (subsection, section FS), 1087
FS (subsection, section SD), 1088
FS (theorem), 1089
FS1 (example), 1090
FS2 (example), 1091
FSAG (example), 1092
FSCF (example), 1093
FTMR (figure), 1094
FTMR (theorem), 1095
FTMRA (figure), 1096
FV (subsection, section TSS), 1097
FVCS (theorem), 1098
G (archetype), 1099
G (theorem), 1100
GE4 (example), 1101
GE6 (example), 1102
GEE (subsection, section IS), 1103
GEK (theorem), 1104
generalized eigenspace
as kernel
theorem GEK, 1105
definition GES, 1106
dimension
theorem DGES, 1107
dimension 4 domain
example GE4, 1108
dimension 6 domain
example GE6, 1109
invariant subspace
theorem GESIS, 1110
nilpotent restriction
theorem RGEN, 1111
nilpotent restrictions, dimension 6 domain
example GENR6, 1112
notation, 1113
generalized eigenspace decomposition
theorem GESD, 1114
generalized eigenvector
definition GEV, 1115
GENR6 (example), 1116
GES (definition), 1117
GES (notation), 1118
GESD (subsection, section JCF), 1119
GESD (theorem), 1120
GESIS (theorem), 1121
GEV (definition), 1122
GFDL (appendix), 1123
GLT (figure), 1124
GME (definition), 1125
goldilocks
theorem G, 1126
Gram-Schmidt
column vectors
theorem GSP, 1127
three vectors
example GSTV, 1128
gram-schmidt
mathematica, 1129
GS (technique, section PT), 1130
GSP (subsection, section O), 1131
GSP (theorem), 1132
GSP.MMA (computation, section MMA), 1133
GSTV (example), 1134
GT (subsection, section PD), 1135
H (archetype), 1136
Hadamard Identity
notation, 1137
Hadamard identity
definition HID, 1138
Hadamard Inverse
notation, 1139
Hadamard inverse
definition HI, 1140
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1141
notation, 1142
Hadamard product
commutativity
theorem HPC, 1143
definition HP, 1144
diagonal matrices
theorem DMMP, 1145
distributivity
theorem HPDAA, 1146
example HP, 1147
identity
theorem HPHID, 1148
inverse
theorem HPHI, 1149
scalar matrix multiplication
theorem HPSMM, 1150
hermitian
definition HM, 1151
Hermitian matrix
inner product
theorem HMIP, 1152
HI (definition), 1153
HI (notation), 1154
HID (definition), 1155
HID (notation), 1156
HISAA (example), 1157
HISAD (example), 1158
HM (definition), 1159
HM (subsection, section MM), 1160
HMEM5 (example), 1161
HMIP (theorem), 1162
HMOE (theorem), 1163
HMRE (theorem), 1164
HMVEI (theorem), 1165
homogeneous system
consistent
theorem HSC, 1166
definition HS, 1167
infinitely many solutions
theorem HMVEI, 1168
homogeneous systems
linear independence, 1169
homogenous system
Archetype C
example AHSAC, 1170
HP (definition), 1171
HP (example), 1172
HP (notation), 1173
HP (section), 1174
HPC (theorem), 1175
HPDAA (theorem), 1176
HPDM (example), 1177
HPHI (theorem), 1178
HPHID (theorem), 1179
HPSMM (theorem), 1180
HS (definition), 1181
HSC (theorem), 1182
HSE (section), 1183
HUSAB (example), 1184
I (archetype), 1185
I (technique, section PT), 1186
IAP (example), 1187
IAR (example), 1188
IAS (example), 1189
IAV (example), 1190
ICBM (theorem), 1191
ICLT (theorem), 1192
identities
technique PI, 1193
identity matrix
determinant, 1194
example IM, 1195
notation, 1196
IDLT (definition), 1197
IDV (definition), 1198
IE (definition), 1199
IE (notation), 1200
IFDVS (theorem), 1201
IILT (theorem), 1202
ILT (definition), 1203
ILT (figure), 1204
ILT (section), 1205
ILTB (theorem), 1206
ILTD (subsection, section ILT), 1207
ILTD (theorem), 1208
ILTIS (theorem), 1209
ILTLI (subsection, section ILT), 1210
ILTLI (theorem), 1211
ILTLT (theorem), 1212
ILTVR (example), 1213
IM (definition), 1214
IM (example), 1215
IM (notation), 1216
IM (subsection, section MISLE), 1217
IM11 (example), 1218
IMILT (theorem), 1219
IMP (definition), 1220
IMR (theorem), 1221
inconsistent linear systems
theorem ISRN, 1222
independent, dependent variables
definition IDV, 1223
indesxstring
example SM2Z7, 1224
example SSET, 1225
index
eigenvalue
definition IE, 1226
notation, 1227
indexstring
theorem DRCMA, 1228
theorem OBUTR, 1229
theorem UMCOB, 1230
induction
technique I, 1231
infinite solution set
example ISSI, 1232
infinite solutions,
example IS, 1233
injective
example IAP, 1234
example IAR, 1235
not
example NIAO, 1236
example NIAQ, 1237
example NIAQR, 1238
not, by dimension
example NIDAU, 1239
polynomials to matrices
example IAV, 1240
injective linear transformation
bases
theorem ILTB, 1241
injective linear transformations
dimension
theorem ILTD, 1242
inner product
anti-commutative
theorem IPAC, 1243
example CSIP, 1244
norm
theorem IPN, 1245
notation, 1246
positive
theorem PIP, 1247
scalar multiplication
theorem IPSM, 1248
vector addition
theorem IPVA, 1249
integers
mod
definition IMP, 1250
mod , field
theorem FIMP, 1251
mod 11
example IM11, 1252
interpolating polynomial
theorem IP, 1253
invariant subspace
definition IS, 1254
eigenspace, 1255
eigenspaces
example EIS, 1256
example TIS, 1257
Jordan block
example ISJB, 1258
kernels of powers
theorem KPIS, 1259
inverse
composition of linear transformations
theorem ICLT, 1260
example CMI, 1261
example MI, 1262
notation, 1263
of a matrix, 1264
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1265
invertible linear transformations
composition
theorem CIVLT, 1266
computing
example CIVLT, 1267
IP (definition), 1268
IP (notation), 1269
IP (subsection, section O), 1270
IP (theorem), 1271
IPAC (theorem), 1272
IPN (theorem), 1273
IPSM (theorem), 1274
IPVA (theorem), 1275
IS (definition), 1276
IS (example), 1277
IS (section), 1278
IS (subsection, section IS), 1279
ISJB (example), 1280
ISMR4 (example), 1281
ISMR6 (example), 1282
isomorphic
multiple vector spaces
example MIVS, 1283
vector spaces
example IVSAV, 1284
isomorphic vector spaces
dimension
theorem IVSED, 1285
example TIVS, 1286
ISRN (theorem), 1287
ISSI (example), 1288
ITMT (theorem), 1289
IV (subsection, section IVLT), 1290
IVLT (definition), 1291
IVLT (section), 1292
IVLT (subsection, section IVLT), 1293
IVLT (subsection, section MR), 1294
IVS (definition), 1295
IVSAV (example), 1296
IVSED (theorem), 1297
J (archetype), 1298
JB (definition), 1299
JB (notation), 1300
JB4 (example), 1301
JCF (definition), 1302
JCF (section), 1303
JCF (subsection, section JCF), 1304
JCF10 (example), 1305
JCFLT (theorem), 1306
Jordan block
definition JB, 1307
nilpotent
theorem NJB, 1308
notation, 1309
size 4
example JB4, 1310
Jordan canonical form
definition JCF, 1311
size 10
example JCF10, 1312
K (archetype), 1313
kernel
injective linear transformation
theorem KILT, 1314
isomorphic to null space
theorem KNSI, 1315
linear transformation
example NKAO, 1316
notation, 1317
of a linear transformation
definition KLT, 1318
pre-image, 1319
subspace
theorem KLTS, 1320
trivial
example TKAP, 1321
via matrix representation
example KVMR, 1322
KILT (theorem), 1323
KLT (definition), 1324
KLT (notation), 1325
KLT (subsection, section ILT), 1326
KLTS (theorem), 1327
KNSI (theorem), 1328
KPI (theorem), 1329
KPIS (theorem), 1330
KPLT (theorem), 1331
KPNLT (example), 1332
KPNLT (theorem), 1333
KVMR (example), 1334
L (archetype), 1335
L (technique, section PT), 1336
LA (subsection, section WILA), 1337
LC (definition), 1338
LC (section), 1339
LC (subsection, section LC), 1340
LC (technique, section PT), 1341
LCCV (definition), 1342
LCM (example), 1343
LDCAA (example), 1344
LDHS (example), 1345
LDP4 (example), 1346
LDRN (example), 1347
LDS (example), 1348
LDS (section), 1349
LDSS (subsection, section LDS), 1350
least squares
minimizes residuals
theorem LSMR, 1351
least squares solution
definition LSS, 1352
left null space
as row space, 1353
definition LNS, 1354
example LNS, 1355
notation, 1356
subspace
theorem LNSMS, 1357
lemma
technique LC, 1358
LI (definition), 1359
LI (section), 1360
LI (subsection, section LISS), 1361
LIC (example), 1362
LICAB (example), 1363
LICV (definition), 1364
LIHS (example), 1365
LIM32 (example), 1366
linear combination
system of equations
example ABLC, 1367
definition LC, 1368
definition LCCV, 1369
example TLC, 1370
linear transformation, 1371
matrices
example LCM, 1372
system of equations
example AALC, 1373
linear combinations
solutions to linear systems
theorem SLSLC, 1374
linear dependence
more vectors than size
theorem MVSLD, 1375
linear independence
definition LI, 1376
definition LICV, 1377
homogeneous systems
theorem LIVHS, 1378
injective linear transformation
theorem ILTLI, 1379
matrices
example LIM32, 1380
orthogonal, 1381
r and n
theorem LIVRN, 1382
linear solve
mathematica, 1383
linear system
consistent
theorem RCLS, 1384
matrix representation
definition LSMR, 1385
notation, 1386
linear systems
notation
example MNSLE, 1387
example NSLE, 1388
linear transformation
polynomials to polynomials
example LTPP, 1389
addition
definition LTA, 1390
theorem MLTLT, 1391
theorem SLTLT, 1392
as matrix multiplication
example ALTMM, 1393
basis of range
example BRLT, 1394
checking
example ALT, 1395
composition
definition LTC, 1396
theorem CLTLT, 1397
defined by a matrix
example LTM, 1398
defined on a basis
example LTDB1, 1399
example LTDB2, 1400
example LTDB3, 1401
theorem LTDB, 1402
definition LT, 1403
identity
definition IDLT, 1404
injection
definition ILT, 1405
inverse
theorem ILTLT, 1406
inverse of inverse
theorem IILT, 1407
invertible
definition IVLT, 1408
example AIVLT, 1409
invertible, injective and surjective
theorem ILTIS, 1410
Jordan canonical form
theorem JCFLT, 1411
kernels of powers
theorem KPLT, 1412
linear combination
theorem LTLC, 1413
matrix of, 1414
example MFLT, 1415
example MOLT, 1416
not
example NLT, 1417
not invertible
example ANILT, 1418
notation, 1419
polynomials to matrices
example LTPM, 1420
rank plus nullity
theorem RPNDD, 1421
restriction
definition LTR, 1422
notation, 1423
scalar multiple
example SMLT, 1424
scalar multiplication
definition LTSM, 1425
spanning range
theorem SSRLT, 1426
sum
example STLT, 1427
surjection
definition SLT, 1428
vector space of, 1429
zero vector
theorem LTTZZ, 1430
linear transformation inverse
via matrix representation
example ILTVR, 1431
linear transformation restriction
on generalized eigenspace
example LTRGE, 1432
linear transformations
compositions
example CTLT, 1433
from matrices
theorem MBLT, 1434
linearly dependent
example LDRN, 1435
via homogeneous system
example LDHS, 1436
linearly dependent columns
Archetype A
example LDCAA, 1437
linearly dependent set
example LDS, 1438
linear combinations within
theorem DLDS, 1439
polynomials
example LDP4, 1440
linearly independent
crazy vector space
example LIC, 1441
extending sets
theorem ELIS, 1442
polynomials
example LIP4, 1443
via homogeneous system
example LIHS, 1444
linearly independent columns
Archetype B
example LICAB, 1445
linearly independent set
example LIS, 1446
example LLDS, 1447
LINM (subsection, section LI), 1448
LINSB (example), 1449
LIP4 (example), 1450
LIS (example), 1451
LISS (section), 1452
LISV (subsection, section LI), 1453
LIVHS (theorem), 1454
LIVRN (theorem), 1455
LLDS (example), 1456
LNS (definition), 1457
LNS (example), 1458
LNS (notation), 1459
LNS (subsection, section FS), 1460
LNSMS (theorem), 1461
lower triangular matrix
definition LTM, 1462
LS.MMA (computation, section MMA), 1463
LSMR (definition), 1464
LSMR (notation), 1465
LSMR (theorem), 1466
LSS (definition), 1467
LT (acronyms, section IVLT), 1468
LT (chapter), 1469
LT (definition), 1470
LT (notation), 1471
LT (section), 1472
LT (subsection, section LT), 1473
LTA (definition), 1474
LTC (definition), 1475
LTC (subsection, section LT), 1476
LTDB (theorem), 1477
LTDB1 (example), 1478
LTDB2 (example), 1479
LTDB3 (example), 1480
LTLC (subsection, section LT), 1481
LTLC (theorem), 1482
LTM (definition), 1483
LTM (example), 1484
LTPM (example), 1485
LTPP (example), 1486
LTR (definition), 1487
LTR (notation), 1488
LTRGE (example), 1489
LTSM (definition), 1490
LTTZZ (theorem), 1491
M (acronyms, section FS), 1492
M (archetype), 1493
M (chapter), 1494
M (definition), 1495
M (notation), 1496
MA (definition), 1497
MA (example), 1498
MA (notation), 1499
MACN (Property), 1500
MAF (Property), 1501
MAP (subsection, section SVD), 1502
mathematica
gram-schmidt (computation), 1503
linear solve (computation), 1504
matrix entry (computation), 1505
matrix inverse (computation), 1506
matrix multiplication (computation), 1507
null space (computation), 1508
row reduce (computation), 1509
transpose of a matrix (computation), 1510
vector form of solutions (computation), 1511
vector linear combinations (computation), 1512
mathematical language
technique L, 1513
matrix
addition
definition MA, 1514
notation, 1515
augmented
definition AM, 1516
column space
definition CSM, 1517
complex conjugate
example CCM, 1518
definition M, 1519
equality
definition ME, 1520
notation, 1521
example AM, 1522
identity
definition IM, 1523
inverse
definition MI, 1524
nonsingular
definition NM, 1525
notation, 1526
of a linear transformation
theorem MLTCV, 1527
product
example PTM, 1528
example PTMEE, 1529
product with vector
definition MVP, 1530
rectangular, 1531
row space
definition RSM, 1532
scalar multiplication
definition MSM, 1533
notation, 1534
singular, 1535
square
definition SQM, 1536
submatrices
example SS, 1537
submatrix
definition SM, 1538
symmetric
definition SYM, 1539
transpose
definition TM, 1540
unitary
definition UM, 1541
unitary is invertible
theorem UMI, 1542
zero
definition ZM, 1543
matrix addition
example MA, 1544
matrix components
notation, 1545
matrix entry
mathematica, 1546
ti83, 1547
ti86, 1548
matrix inverse
Archetype B, 1549
computation
theorem CINM, 1550
mathematica, 1551
nonsingular matrix
theorem NI, 1552
of a matrix inverse
theorem MIMI, 1553
one-sided
theorem OSIS, 1554
product
theorem SS, 1555
scalar multiple
theorem MISM, 1556
size 2 matrices
theorem TTMI, 1557
transpose
theorem MIT, 1558
uniqueness
theorem MIU, 1559
matrix multiplication
adjoints
theorem MMAD, 1560
associativity
theorem MMA, 1561
complex conjugation
theorem MMCC, 1562
definition MM, 1563
distributivity
theorem MMDAA, 1564
entry-by-entry
theorem EMP, 1565
identity matrix
theorem MMIM, 1566
inner product
theorem MMIP, 1567
mathematica, 1568
noncommutative
example MMNC, 1569
scalar matrix multiplication
theorem MMSMM, 1570
systems of linear equations
theorem SLEMM, 1571
transposes
theorem MMT, 1572
zero matrix
theorem MMZM, 1573
matrix product
as composition of linear transformations
example MPMR, 1574
matrix representation
basis of eigenvectors
example MRBE, 1575
composition of linear transformations
theorem MRCLT, 1576
definition MR, 1577
invertible
theorem IMR, 1578
multiple of a linear transformation
theorem MRMLT, 1579
notation, 1580
restriction to generalized eigenspace
theorem MRRGE, 1581
sum of linear transformations
theorem MRSLT, 1582
theorem FTMR, 1583
upper triangular
theorem UTMR, 1584
matrix representations
converting with change-of-basis
example MRCM, 1585
example OLTTR, 1586
matrix scalar multiplication
example MSM, 1587
matrix vector space
dimension
theorem DM, 1588
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1589
matrix-vector product
example MTV, 1590
notation, 1591
MBC (example), 1592
MBLT (theorem), 1593
MC (notation), 1594
MCC (subsection, section MO), 1595
MCCN (Property), 1596
MCF (Property), 1597
MCN (definition), 1598
MCN (subsection, section CNO), 1599
MCSM (example), 1600
MCT (theorem), 1601
MD (chapter), 1602
ME (definition), 1603
ME (notation), 1604
ME (subsection, section PEE), 1605
ME (technique, section PT), 1606
ME (theorem), 1607
ME.MMA (computation, section MMA), 1608
ME.TI83 (computation, section TI83), 1609
ME.TI86 (computation, section TI86), 1610
MEASM (subsection, section MO), 1611
MFLT (example), 1612
MI (definition), 1613
MI (example), 1614
MI (notation), 1615
MI.MMA (computation, section MMA), 1616
MICN (Property), 1617
MIF (Property), 1618
MIMI (theorem), 1619
MINM (section), 1620
MISLE (section), 1621
MISM (theorem), 1622
MIT (theorem), 1623
MIU (theorem), 1624
MIVS (example), 1625
MLT (subsection, section LT), 1626
MLTCV (theorem), 1627
MLTLT (theorem), 1628
MM (definition), 1629
MM (section), 1630
MM (subsection, section MM), 1631
MM.MMA (computation, section MMA), 1632
MMA (section), 1633
MMA (theorem), 1634
MMAD (theorem), 1635
MMCC (theorem), 1636
MMDAA (theorem), 1637
MMEE (subsection, section MM), 1638
MMIM (theorem), 1639
MMIP (theorem), 1640
MMNC (example), 1641
MMSMM (theorem), 1642
MMT (theorem), 1643
MMZM (theorem), 1644
MNEM (theorem), 1645
MNSLE (example), 1646
MO (section), 1647
MOLT (example), 1648
more variables than equations
example OSGMD, 1649
theorem CMVEI, 1650
MPMR (example), 1651
MR (definition), 1652
MR (notation), 1653
MR (section), 1654
MRBE (example), 1655
MRCB (theorem), 1656
MRCLT (figure), 1657
MRCLT (theorem), 1658
MRCM (example), 1659
MRMLT (theorem), 1660
MRRGE (theorem), 1661
MRS (subsection, section CB), 1662
MRSLT (theorem), 1663
MSCN (example), 1664
MSM (definition), 1665
MSM (example), 1666
MSM (notation), 1667
MTV (example), 1668
multiplicative associativity
complex numbers
Property MACN, 1669
multiplicative closure
complex numbers
Property MCCN, 1670
field
Property MCF, 1671
multiplicative commuativity
complex numbers
Property CMCN, 1672
multiplicative inverse
complex numbers
Property MICN, 1673
MVNSE (subsection, section RREF), 1674
MVP (definition), 1675
MVP (notation), 1676
MVP (subsection, section MM), 1677
MVSLD (theorem), 1678
MWIAA (example), 1679
N (archetype), 1680
N (subsection, section O), 1681
N (technique, section PT), 1682
NDMS4 (example), 1683
negation of statements
technique N, 1684
NEM (theorem), 1685
NI (theorem), 1686
NIAO (example), 1687
NIAQ (example), 1688
NIAQR (example), 1689
NIDAU (example), 1690
nilpotent
linear transformation
definition NLT, 1691
NILT (figure), 1692
NJB (theorem), 1693
NJB5 (example), 1694
NKAO (example), 1695
NLT (definition), 1696
NLT (example), 1697
NLT (section), 1698
NLT (subsection, section NLT), 1699
NLTFO (subsection, section LT), 1700
NM (definition), 1701
NM (example), 1702
NM (section), 1703
NM (subsection, section NM), 1704
NM (subsection, section OD), 1705
NM62 (example), 1706
NM64 (example), 1707
NM83 (example), 1708
NME1 (theorem), 1709
NME2 (theorem), 1710
NME3 (theorem), 1711
NME4 (theorem), 1712
NME5 (theorem), 1713
NME6 (theorem), 1714
NME7 (theorem), 1715
NME8 (theorem), 1716
NME9 (theorem), 1717
NMI (subsection, section MINM), 1718
NMLIC (theorem), 1719
NMPEM (theorem), 1720
NMRRI (theorem), 1721
NMTNS (theorem), 1722
NMUS (theorem), 1723
NOILT (theorem), 1724
NOLT (definition), 1725
NOLT (notation), 1726
NOM (definition), 1727
NOM (notation), 1728
nonsingular
columns as basis
theorem CNMB, 1729
nonsingular matrices
linearly independent columns
theorem NMLIC, 1730
nonsingular matrix
Archetype B
example NM, 1731
column space, 1732
elemntary matrices
theorem NMPEM, 1733
equivalences
theorem NME1, 1734
theorem NME2, 1735
theorem NME3, 1736
theorem NME4, 1737
theorem NME5, 1738
theorem NME6, 1739
theorem NME7, 1740
theorem NME8, 1741
theorem NME9, 1742
matrix inverse, 1743
null space
example NSNM, 1744
nullity, 1745
product of nonsingular matrices
theorem NPNT, 1746
rank
theorem RNNM, 1747
row-reduced
theorem NMRRI, 1748
trivial null space
theorem NMTNS, 1749
unique solutions
theorem NMUS, 1750
nonsingular matrix, row-reduced
example NSR, 1751
norm
example CNSV, 1752
inner product, 1753
notation, 1754
normal matrix
definition NRML, 1755
example ANM, 1756
orthonormal basis, 1757
notation
A, 1758
AM, 1759
C, 1760
CCCV, 1761
CCM, 1762
CCN, 1763
CNA, 1764
CNE, 1765
CNM, 1766
CSM, 1767
CV, 1768
CVA, 1769
CVC, 1770
CVE, 1771
CVSM, 1772
D, 1773
DM, 1774
DS, 1775
ELEM, 1776
ES, 1777
GES, 1778
HI, 1779
HID, 1780
HP, 1781
IE, 1782
IM, 1783
IP, 1784
JB, 1785
KLT, 1786
LNS, 1787
LSMR, 1788
LT, 1789
LTR, 1790
M, 1791
MA, 1792
MC, 1793
ME, 1794
MI, 1795
MR, 1796
MSM, 1797
MVP, 1798
NOLT, 1799
NOM, 1800
NSM, 1801
NV, 1802
RLT, 1803
RO, 1804
ROLT, 1805
ROM, 1806
RREFA, 1807
RSM, 1808
SC, 1809
SE, 1810
SETM, 1811
SI, 1812
SM, 1813
SRM, 1814
SSET, 1815
SSV, 1816
SU, 1817
SUV, 1818
T, 1819
TM, 1820
VR, 1821
VSCV, 1822
VSM, 1823
ZCV, 1824
ZM, 1825
notation for a linear system
example NSE, 1826
NPNT (theorem), 1827
NRFO (subsection, section MR), 1828
NRML (definition), 1829
NRREF (example), 1830
NS.MMA (computation, section MMA), 1831
NSAO (example), 1832
NSAQ (example), 1833
NSAQR (example), 1834
NSC2A (example), 1835
NSC2S (example), 1836
NSC2Z (example), 1837
NSDAT (example), 1838
NSDS (example), 1839
NSE (example), 1840
NSEAI (example), 1841
NSLE (example), 1842
NSLIL (example), 1843
NSM (definition), 1844
NSM (notation), 1845
NSM (subsection, section HSE), 1846
NSMS (theorem), 1847
NSNM (example), 1848
NSNM (subsection, section NM), 1849
NSR (example), 1850
NSS (example), 1851
NSSLI (subsection, section LI), 1852
Null space
as a span
example NSDS, 1853
null space
Archetype I
example NSEAI, 1854
basis
theorem BNS, 1855
computation
example CNS1, 1856
example CNS2, 1857
isomorphic to kernel, 1858
linearly independent basis
example LINSB, 1859
mathematica, 1860
matrix
definition NSM, 1861
nonsingular matrix, 1862
notation, 1863
singular matrix, 1864
spanning set
example SSNS, 1865
theorem SSNS, 1866
subspace
theorem NSMS, 1867
null space span, linearly independent
Archetype L
example NSLIL, 1868
nullity
computing, 1869
injective linear transformation
theorem NOILT, 1870
linear transformation
definition NOLT, 1871
matrix, 1872
definition NOM, 1873
notation, 1874, 1875
square matrix, 1876
NV (definition), 1877
NV (notation), 1878
NVM (theorem), 1879
O (archetype), 1880
O (Property), 1881
O (section), 1882
OBC (subsection, section B), 1883
OBNM (theorem), 1884
OBUTR (theorem), 1885
OC (Property), 1886
OCN (Property), 1887
OD (section), 1888
OD (subsection, section OD), 1889
OD (theorem), 1890
OF (Property), 1891
OLTTR (example), 1892
OM (Property), 1893
one
column vectors
Property OC, 1894
complex numbers
Property OCN, 1895
field
Property OF, 1896
matrices
Property OM, 1897
vectors
Property O, 1898
ONFV (example), 1899
ONS (definition), 1900
ONTV (example), 1901
orthogonal
linear independence
theorem OSLI, 1902
set
example AOS, 1903
set of vectors
definition OSV, 1904
vector pairs
definition OV, 1905
orthogonal vectors
example TOV, 1906
orthonormal
definition ONS, 1907
matrix columns
example OSMC, 1908
orthonormal basis
normal matrix
theorem OBNM, 1909
orthonormal diagonalization
theorem OD, 1910
orthonormal set
four vectors
example ONFV, 1911
three vectors
example ONTV, 1912
OSGMD (example), 1913
OSIS (theorem), 1914
OSLI (theorem), 1915
OSMC (example), 1916
OSV (definition), 1917
OV (definition), 1918
OV (subsection, section O), 1919
P (appendix), 1920
P (archetype), 1921
P (technique, section PT), 1922
particular solutions
example PSHS, 1923
PCNA (theorem), 1924
PCVS (example), 1925
PD (section), 1926
PDM (section), 1927
PDM (theorem), 1928
PEE (section), 1929
PEEF (theorem), 1930
PI (definition), 1931
PI (subsection, section LT), 1932
PI (technique, section PT), 1933
PIP (theorem), 1934
PM (example), 1935
PM (subsection, section EE), 1936
PMI (subsection, section MISLE), 1937
PMM (subsection, section MM), 1938
PMR (subsection, section MR), 1939
PNLT (subsection, section NLT), 1940
POD (section), 1941
polar decomposition
theorem PDM, 1942
polynomial
of a matrix
example PM, 1943
polynomial vector space
dimension
theorem DP, 1944
positive semi-definite
creating
theorem CPSM, 1945
positive semi-definite matrix
definition PSM, 1946
eigenvalues
theorem EPSM, 1947
practice
technique P, 1948
pre-image
definition PI, 1949
kernel
theorem KPI, 1950
pre-images
example SPIAS, 1951
principal axis theorem, 1952
product of triangular matrices
theorem PTMT, 1953
Property
AA, 1954
AAC, 1955
AACN, 1956
AAF, 1957
AAM, 1958
AC, 1959
ACC, 1960
ACCN, 1961
ACF, 1962
ACM, 1963
AI, 1964
AIC, 1965
AICN, 1966
AIF, 1967
AIM, 1968
C, 1969
CACN, 1970
CAF, 1971
CC, 1972
CM, 1973
CMCN, 1974
CMF, 1975
DCN, 1976
DF, 1977
DMAM, 1978
DSA, 1979
DSAC, 1980
DSAM, 1981
DVA, 1982
DVAC, 1983
MACN, 1984
MAF, 1985
MCCN, 1986
MCF, 1987
MICN, 1988
MIF, 1989
O, 1990
OC, 1991
OCN, 1992
OF, 1993
OM, 1994
SC, 1995
SCC, 1996
SCM, 1997
SMA, 1998
SMAC, 1999
SMAM, 2000
Z, 2001
ZC, 2002
ZCN, 2003
ZF, 2004
ZM, 2005
PSHS (example), 2006
PSHS (subsection, section LC), 2007
PSM (definition), 2008
PSM (section), 2009
PSM (subsection, section PSM), 2010
PSM (subsection, section SD), 2011
PSMSR (theorem), 2012
PSPHS (theorem), 2013
PSS (subsection, section SSLE), 2014
PSSD (theorem), 2015
PSSLS (theorem), 2016
PT (section), 2017
PTFP (example), 2018
PTM (example), 2019
PTMEE (example), 2020
PTMT (theorem), 2021
Q (archetype), 2022
R (acronyms, section JCF), 2023
R (archetype), 2024
R (chapter), 2025
range
full
example FRAN, 2026
isomorphic to column space
theorem RCSI, 2027
linear transformation
example RAO, 2028
notation, 2029
of a linear transformation
definition RLT, 2030
pre-image
theorem RPI, 2031
subspace
theorem RLTS, 2032
surjective linear transformation
theorem RSLT, 2033
via matrix representation
example RVMR, 2034
rank
computing
theorem CRN, 2035
linear transformation
definition ROLT, 2036
matrix
definition ROM, 2037
example RNM, 2038
notation, 2039, 2040
of transpose
example RRTI, 2041
square matrix
example RNSM, 2042
surjective linear transformation
theorem ROSLT, 2043
transpose
theorem RMRT, 2044
rank one decomposition
size 2
example ROD2, 2045
size 4
example ROD4, 2046
theorem ROD, 2047
rank+nullity
theorem RPNC, 2048
RAO (example), 2049
RCLS (theorem), 2050
RCSI (theorem), 2051
RD (subsection, section VS), 2052
RDS (theorem), 2053
READ (subsection, section B), 2054
READ (subsection, section CB), 2055
READ (subsection, section CRS), 2056
READ (subsection, section D), 2057
READ (subsection, section DM), 2058
READ (subsection, section EE), 2059
READ (subsection, section FS), 2060
READ (subsection, section HSE), 2061
READ (subsection, section ILT), 2062
READ (subsection, section IVLT), 2063
READ (subsection, section LC), 2064
READ (subsection, section LDS), 2065
READ (subsection, section LI), 2066
READ (subsection, section LISS), 2067
READ (subsection, section LT), 2068
READ (subsection, section MINM), 2069
READ (subsection, section MISLE), 2070
READ (subsection, section MM), 2071
READ (subsection, section MO), 2072
READ (subsection, section MR), 2073
READ (subsection, section NM), 2074
READ (subsection, section O), 2075
READ (subsection, section PD), 2076
READ (subsection, section PDM), 2077
READ (subsection, section PEE), 2078
READ (subsection, section RREF), 2079
READ (subsection, section S), 2080
READ (subsection, section SD), 2081
READ (subsection, section SLT), 2082
READ (subsection, section SS), 2083
READ (subsection, section SSLE), 2084
READ (subsection, section TSS), 2085
READ (subsection, section VO), 2086
READ (subsection, section VR), 2087
READ (subsection, section VS), 2088
READ (subsection, section WILA), 2089
reduced row-echelon form
analysis
notation, 2090
definition RREF, 2091
example NRREF, 2092
example RREF, 2093
extended
definition EEF, 2094
notation
example RREFN, 2095
unique
theorem RREFU, 2096
reducing a span
example RSC5, 2097
relation of linear dependence
definition RLD, 2098
definition RLDCV, 2099
REM (definition), 2100
REMEF (theorem), 2101
REMES (theorem), 2102
REMRS (theorem), 2103
RES (example), 2104
RGEN (theorem), 2105
RLD (definition), 2106
RLDCV (definition), 2107
RLT (definition), 2108
RLT (notation), 2109
RLT (subsection, section IS), 2110
RLT (subsection, section SLT), 2111
RLTS (theorem), 2112
RMRT (theorem), 2113
RNLT (subsection, section IVLT), 2114
RNM (example), 2115
RNM (subsection, section D), 2116
RNNM (subsection, section D), 2117
RNNM (theorem), 2118
RNSM (example), 2119
RO (definition), 2120
RO (notation), 2121
RO (subsection, section RREF), 2122
ROD (section), 2123
ROD (theorem), 2124
ROD2 (example), 2125
ROD4 (example), 2126
ROLT (definition), 2127
ROLT (notation), 2128
ROM (definition), 2129
ROM (notation), 2130
ROSLT (theorem), 2131
row operations
definition RO, 2132
elementary matrices, 2133, 2134
notation, 2135
row reduce
mathematica, 2136
ti83, 2137
ti86, 2138
row space
Archetype I
example RSAI, 2139
as column space, 2140
basis
example RSB, 2141
theorem BRS, 2142
matrix, 2143
notation, 2144
row-equivalent matrices
theorem REMRS, 2145
subspace
theorem RSMS, 2146
row-equivalent matrices
definition REM, 2147
example TREM, 2148
row space, 2149
row spaces
example RSREM, 2150
theorem REMES, 2151
row-reduce
the verb
definition RR, 2152
row-reduced matrices
theorem REMEF, 2153
RPI (theorem), 2154
RPNC (theorem), 2155
RPNDD (theorem), 2156
RR (definition), 2157
RR.MMA (computation, section MMA), 2158
RR.TI83 (computation, section TI83), 2159
RR.TI86 (computation, section TI86), 2160
RREF (definition), 2161
RREF (example), 2162
RREF (section), 2163
RREF (subsection, section RREF), 2164
RREFA (notation), 2165
RREFN (example), 2166
RREFU (theorem), 2167
RRTI (example), 2168
RS (example), 2169
RSAI (example), 2170
RSB (example), 2171
RSC5 (example), 2172
RSLT (theorem), 2173
RSM (definition), 2174
RSM (notation), 2175
RSM (subsection, section CRS), 2176
RSMS (theorem), 2177
RSNS (example), 2178
RSREM (example), 2179
RSSC4 (example), 2180
RT (subsection, section PD), 2181
RVMR (example), 2182
S (archetype), 2183
S (definition), 2184
S (example), 2185
S (section), 2186
SAA (example), 2187
SAB (example), 2188
SABMI (example), 2189
SAE (example), 2190
SAN (example), 2191
SAR (example), 2192
SAS (section), 2193
SAV (example), 2194
SC (definition), 2195
SC (example), 2196
SC (notation), 2197
SC (Property), 2198
SC (subsection, section S), 2199
SC (subsection, section SET), 2200
SC3 (example), 2201
SCAA (example), 2202
SCAB (example), 2203
SCAD (example), 2204
scalar closure
column vectors
Property SCC, 2205
matrices
Property SCM, 2206
vectors
Property SC, 2207
scalar multiple
matrix inverse, 2208
scalar multiplication
zero scalar
theorem ZSSM, 2209
zero vector
theorem ZVSM, 2210
zero vector result
theorem SMEZV, 2211
scalar multiplication associativity
column vectors
Property SMAC, 2212
matrices
Property SMAM, 2213
vectors
Property SMA, 2214
SCB (theorem), 2215
SCC (Property), 2216
SCM (Property), 2217
SD (section), 2218
SDS (example), 2219
SE (definition), 2220
SE (notation), 2221
secret sharing
6 ways
example SS6W, 2222
SEE (example), 2223
SEEF (example), 2224
SER (theorem), 2225
set
cardinality
definition C, 2226
example CS, 2227
notation, 2228
complement
definition SC, 2229
example SC, 2230
notation, 2231
definition SET, 2232
empty
definition ES, 2233
equality
definition SE, 2234
notation, 2235
intersection
definition SI, 2236
example SI, 2237
notation, 2238
membership
example SETM, 2239
notation, 2240
size, 2241
subset, 2242
union
definition SU, 2243
example SU, 2244
notation, 2245
SET (definition), 2246
SET (section), 2247
SETM (example), 2248
SETM (notation), 2249
shoes, 2250
SHS (subsection, section HSE), 2251
SI (definition), 2252
SI (example), 2253
SI (notation), 2254
SI (subsection, section IVLT), 2255
SIM (definition), 2256
similar matrices
equal eigenvalues
example EENS, 2257
eual eigenvalues
theorem SMEE, 2258
example SMS3, 2259
example SMS5, 2260
similarity
definition SIM, 2261
equivalence relation
theorem SER, 2262
singular matrix
Archetype A
example S, 2263
null space
example NSS, 2264
singular matrix, row-reduced
example SRR, 2265
singular value decomposition
theorem SVD, 2266
singular values
definition SV, 2267
SLE (acronyms, section NM), 2268
SLE (chapter), 2269
SLE (definition), 2270
SLE (subsection, section SSLE), 2271
SLELT (subsection, section IVLT), 2272
SLEMM (theorem), 2273
SLSLC (theorem), 2274
SLT (definition), 2275
SLT (section), 2276
SLTB (theorem), 2277
SLTD (subsection, section SLT), 2278
SLTD (theorem), 2279
SLTLT (theorem), 2280
SM (definition), 2281
SM (notation), 2282
SM (subsection, section SD), 2283
SM2Z7 (example), 2284
SM32 (example), 2285
SMA (Property), 2286
SMAC (Property), 2287
SMAM (Property), 2288
SMEE (theorem), 2289
SMEZV (theorem), 2290
SMLT (example), 2291
SMS (theorem), 2292
SMS3 (example), 2293
SMS5 (example), 2294
SMZD (theorem), 2295
SMZE (theorem), 2296
SNCM (theorem), 2297
SO (subsection, section SET), 2298
socks, 2299
SOL (subsection, section B), 2300
SOL (subsection, section CB), 2301
SOL (subsection, section CRS), 2302
SOL (subsection, section D), 2303
SOL (subsection, section DM), 2304
SOL (subsection, section EE), 2305
SOL (subsection, section F), 2306
SOL (subsection, section FS), 2307
SOL (subsection, section HSE), 2308
SOL (subsection, section ILT), 2309
SOL (subsection, section IVLT), 2310
SOL (subsection, section LC), 2311
SOL (subsection, section LDS), 2312
SOL (subsection, section LI), 2313
SOL (subsection, section LISS), 2314
SOL (subsection, section LT), 2315
SOL (subsection, section MINM), 2316
SOL (subsection, section MISLE), 2317
SOL (subsection, section MM), 2318
SOL (subsection, section MO), 2319
SOL (subsection, section MR), 2320
SOL (subsection, section NM), 2321
SOL (subsection, section O), 2322
SOL (subsection, section PD), 2323
SOL (subsection, section PDM), 2324
SOL (subsection, section PEE), 2325
SOL (subsection, section RREF), 2326
SOL (subsection, section S), 2327
SOL (subsection, section SD), 2328
SOL (subsection, section SLT), 2329
SOL (subsection, section SS), 2330
SOL (subsection, section SSLE), 2331
SOL (subsection, section T), 2332
SOL (subsection, section TSS), 2333
SOL (subsection, section VO), 2334
SOL (subsection, section VR), 2335
SOL (subsection, section VS), 2336
SOL (subsection, section WILA), 2337
solution set
Archetype A
example SAA, 2338
archetype E
example SAE, 2339
theorem PSPHS, 2340
solution sets
possibilities
theorem PSSLS, 2341
solution vector
definition SOLV, 2342
SOLV (definition), 2343
solving homogeneous system
Archetype A
example HISAA, 2344
Archetype B
example HUSAB, 2345
Archetype D
example HISAD, 2346
solving nonlinear equations
example STNE, 2347
SP4 (example), 2348
span
basic
example ABS, 2349
basis
theorem BS, 2350
definition SS, 2351
definition SSCV, 2352
improved
example IAS, 2353
notation, 2354
reducing
example RSSC4, 2355
reduction
example RS, 2356
removing vectors
example COV, 2357
reworking elements
example RES, 2358
set of polynomials
example SSP, 2359
subspace
theorem SSS, 2360
span of columns
Archetype A
example SCAA, 2361
Archetype B
example SCAB, 2362
Archetype D
example SCAD, 2363
spanning set
crazy vector space
example SSC, 2364
definition TSVS, 2365
matrices
example SSM22, 2366
more vectors
theorem SSLD, 2367
polynomials
example SSP4, 2368
SPIAS (example), 2369
SQM (definition), 2370
square root
eigenvalues, eigenspaces
theorem EESR, 2371
matrix
definition SRM, 2372
notation, 2373
positive semi-definite matrix
theorem PSMSR, 2374
unique
theorem USR, 2375
SR (section), 2376
SRM (definition), 2377
SRM (notation), 2378
SRM (subsection, section SR), 2379
SRR (example), 2380
SS (definition), 2381
SS (example), 2382
SS (section), 2383
SS (subsection, section LISS), 2384
SS (theorem), 2385
SS6W (example), 2386
SSC (example), 2387
SSCV (definition), 2388
SSET (definition), 2389
SSET (example), 2390
SSET (notation), 2391
SSLD (theorem), 2392
SSLE (section), 2393
SSM22 (example), 2394
SSNS (example), 2395
SSNS (subsection, section SS), 2396
SSNS (theorem), 2397
SSP (example), 2398
SSP4 (example), 2399
SSRLT (theorem), 2400
SSS (theorem), 2401
SSSLT (subsection, section SLT), 2402
SSV (notation), 2403
SSV (subsection, section SS), 2404
standard unit vector
notation, 2405
starting proofs
technique GS, 2406
STLT (example), 2407
STNE (example), 2408
SU (definition), 2409
SU (example), 2410
SU (notation), 2411
submatrix
notation, 2412
subset
definition SSET, 2413
notation, 2414
subspace
as null space
example RSNS, 2415
characterized
example ASC, 2416
definition S, 2417
in
example SP4, 2418
not, additive closure
example NSC2A, 2419
not, scalar closure
example NSC2S, 2420
not, zero vector
example NSC2Z, 2421
testing
theorem TSS, 2422
trivial
definition TS, 2423
verification
example SC3, 2424
example SM32, 2425
subspaces
equal dimension
theorem EDYES, 2426
surjective
Archetype N
example SAN, 2427
example SAR, 2428
not
example NSAQ, 2429
example NSAQR, 2430
not, Archetype O
example NSAO, 2431
not, by dimension
example NSDAT, 2432
polynomials to matrices
example SAV, 2433
surjective linear transformation
bases
theorem SLTB, 2434
surjective linear transformations
dimension
theorem SLTD, 2435
SUV (definition), 2436
SUV (notation), 2437
SUVB (theorem), 2438
SUVOS (example), 2439
SV (definition), 2440
SVD (section), 2441
SVD (subsection, section SVD), 2442
SVD (theorem), 2443
SVP4 (example), 2444
SYM (definition), 2445
SYM (example), 2446
symmetric matrices
theorem SMS, 2447
symmetric matrix
example SYM, 2448
system of equations
vector equality
example VESE, 2449
system of linear equations
definition SLE, 2450
T (archetype), 2451
T (definition), 2452
T (notation), 2453
T (part), 2454
T (section), 2455
T (technique, section PT), 2456
TCSD (example), 2457
TD (section), 2458
TD (subsection, section TD), 2459
TD (theorem), 2460
TD4 (example), 2461
TDEE (theorem), 2462
TDEE6 (example), 2463
TDSSE (example), 2464
TDSSE (subsection, section TD), 2465
technique
C, 2466
CD, 2467
CP, 2468
CV, 2469
D, 2470
DC, 2471
E, 2472
GS, 2473
I, 2474
L, 2475
LC, 2476
ME, 2477
N, 2478
P, 2479
PI, 2480
T, 2481
U, 2482
theorem
AA, 2483
AIP, 2484
AISM, 2485
AIU, 2486
AMA, 2487
AMSM, 2488
BCS, 2489
BIS, 2490
BNS, 2491
BRS, 2492
BS, 2493
CB, 2494
CCM, 2495
CCRA, 2496
CCRM, 2497
CCT, 2498
CFDVS, 2499
CFNLT, 2500
CHT, 2501
CILTI, 2502
CINM, 2503
CIVLT, 2504
CLI, 2505
CLTLT, 2506
CMVEI, 2507
CNMB, 2508
COB, 2509
CPSM, 2510
CRMA, 2511
CRMSM, 2512
CRN, 2513
CRSM, 2514
CRVA, 2515
CSCS, 2516
CSLTS, 2517
CSMS, 2518
CSNM, 2519
CSRN, 2520
CSRST, 2521
CSS, 2522
CUMOS, 2523
DC, 2524
DCM, 2525
DCP, 2526
DEC, 2527
DED, 2528
DEM, 2529
DEMMM, 2530
DER, 2531
DERC, 2532
DFS, 2533
DGES, 2534
DIM, 2535
DLDS, 2536
DM, 2537
DMFE, 2538
DMHP, 2539
DMMP, 2540
DMST, 2541
DNLT, 2542
DP, 2543
DRCM, 2544
DRCMA, 2545
DRCS, 2546
DRMM, 2547
DSD, 2548
DSFB, 2549
DSFOS, 2550
DSLI, 2551
DSZI, 2552
DSZV, 2553
DT, 2554
DVM, 2555
DZRC, 2556
EDELI, 2557
EDYES, 2558
EEMAP, 2559
EER, 2560
EESR, 2561
EIM, 2562
EIS, 2563
ELIS, 2564
EMDRO, 2565
EMHE, 2566
EMMVP, 2567
EMN, 2568
EMNS, 2569
EMP, 2570
EMRCP, 2571
EMS, 2572
ENLT, 2573
EOMP, 2574
EOPSS, 2575
EPM, 2576
EPSM, 2577
ERMCP, 2578
ESMM, 2579
ETM, 2580
FIMP, 2581
FS, 2582
FTMR, 2583
FVCS, 2584
G, 2585
GEK, 2586
GESD, 2587
GESIS, 2588
GSP, 2589
HMIP, 2590
HMOE, 2591
HMRE, 2592
HMVEI, 2593
HPC, 2594
HPDAA, 2595
HPHI, 2596
HPHID, 2597
HPSMM, 2598
HSC, 2599
ICBM, 2600
ICLT, 2601
IFDVS, 2602
IILT, 2603
ILTB, 2604
ILTD, 2605
ILTIS, 2606
ILTLI, 2607
ILTLT, 2608
IMILT, 2609
IMR, 2610
IP, 2611
IPAC, 2612
IPN, 2613
IPSM, 2614
IPVA, 2615
ISRN, 2616
ITMT, 2617
IVSED, 2618
JCFLT, 2619
KILT, 2620
KLTS, 2621
KNSI, 2622
KPI, 2623
KPIS, 2624
KPLT, 2625
KPNLT, 2626
LIVHS, 2627
LIVRN, 2628
LNSMS, 2629
LSMR, 2630
LTDB, 2631
LTLC, 2632
LTTZZ, 2633
MBLT, 2634
MCT, 2635
ME, 2636
MIMI, 2637
MISM, 2638
MIT, 2639
MIU, 2640
MLTCV, 2641
MLTLT, 2642
MMA, 2643
MMAD, 2644
MMCC, 2645
MMDAA, 2646
MMIM, 2647
MMIP, 2648
MMSMM, 2649
MMT, 2650
MMZM, 2651
MNEM, 2652
MRCB, 2653
MRCLT, 2654
MRMLT, 2655
MRRGE, 2656
MRSLT, 2657
MVSLD, 2658
NEM, 2659
NI, 2660
NJB, 2661
NME1, 2662
NME2, 2663
NME3, 2664
NME4, 2665
NME5, 2666
NME6, 2667
NME7, 2668
NME8, 2669
NME9, 2670
NMLIC, 2671
NMPEM, 2672
NMRRI, 2673
NMTNS, 2674
NMUS, 2675
NOILT, 2676
NPNT, 2677
NSMS, 2678
NVM, 2679
OBNM, 2680
OBUTR, 2681
OD, 2682
OSIS, 2683
OSLI, 2684
PCNA, 2685
PDM, 2686
PEEF, 2687
PIP, 2688
PSMSR, 2689
PSPHS, 2690
PSSD, 2691
PSSLS, 2692
PTMT, 2693
RCLS, 2694
RCSI, 2695
RDS, 2696
REMEF, 2697
REMES, 2698
REMRS, 2699
RGEN, 2700
RLTS, 2701
RMRT, 2702
RNNM, 2703
ROD, 2704
ROSLT, 2705
RPI, 2706
RPNC, 2707
RPNDD, 2708
RREFU, 2709
RSLT, 2710
RSMS, 2711
SCB, 2712
SER, 2713
SLEMM, 2714
SLSLC, 2715
SLTB, 2716
SLTD, 2717
SLTLT, 2718
SMEE, 2719
SMEZV, 2720
SMS, 2721
SMZD, 2722
SMZE, 2723
SNCM, 2724
SS, 2725
SSLD, 2726
SSNS, 2727
SSRLT, 2728
SSS, 2729
SUVB, 2730
SVD, 2731
TD, 2732
TDEE, 2733
technique T, 2734
TIST, 2735
TL, 2736
TMA, 2737
TMSM, 2738
TSE, 2739
TSRM, 2740
TSS, 2741
TT, 2742
TTMI, 2743
UMCOB, 2744
UMI, 2745
UMPIP, 2746
USR, 2747
UTMR, 2748
VFSLS, 2749
VRI, 2750
VRILT, 2751
VRLT, 2752
VRRB, 2753
VRS, 2754
VSLT, 2755
VSPCV, 2756
VSPM, 2757
ZSSM, 2758
ZVSM, 2759
ZVU, 2760
ti83
matrix entry (computation), 2761
row reduce (computation), 2762
vector linear combinations (computation), 2763
TI83 (section), 2764
ti86
matrix entry (computation), 2765
row reduce (computation), 2766
transpose of a matrix (computation), 2767
vector linear combinations (computation), 2768
TI86 (section), 2769
TIS (example), 2770
TIST (theorem), 2771
TIVS (example), 2772
TKAP (example), 2773
TL (theorem), 2774
TLC (example), 2775
TM (definition), 2776
TM (example), 2777
TM (notation), 2778
TM (subsection, section OD), 2779
TM.MMA (computation, section MMA), 2780
TM.TI86 (computation, section TI86), 2781
TMA (theorem), 2782
TMP (example), 2783
TMSM (theorem), 2784
TOV (example), 2785
trace
definition T, 2786
linearity
theorem TL, 2787
matrix multiplication
theorem TSRM, 2788
notation, 2789
similarity
theorem TIST, 2790
sum of eigenvalues
theorem TSE, 2791
trail mix
example TMP, 2792
transpose
matrix scalar multiplication
theorem TMSM, 2793
example TM, 2794
matrix addition
theorem TMA, 2795
matrix inverse, 2796, 2797
notation, 2798
scalar multiplication, 2799
transpose of a matrix
mathematica, 2800
ti86, 2801
transpose of a transpose
theorem TT, 2802
TREM (example), 2803
triangular decomposition
entry by entry, size 6
example TDEE6, 2804
entry by entry
theorem TDEE, 2805
size 4
example TD4, 2806
solving systems of equations
example TDSSE, 2807
theorem TD, 2808
triangular matrix
inverse
theorem ITMT, 2809
trivial solution
system of equations
definition TSHSE, 2810
TS (definition), 2811
TS (subsection, section S), 2812
TSE (theorem), 2813
TSHSE (definition), 2814
TSM (subsection, section MO), 2815
TSRM (theorem), 2816
TSS (section), 2817
TSS (subsection, section S), 2818
TSS (theorem), 2819
TSVS (definition), 2820
TT (theorem), 2821
TTMI (theorem), 2822
TTS (example), 2823
typical systems,
example TTS, 2824
U (archetype), 2825
U (technique, section PT), 2826
UM (definition), 2827
UM (subsection, section MINM), 2828
UM3 (example), 2829
UMCOB (theorem), 2830
UMI (theorem), 2831
UMPIP (theorem), 2832
unique solution,
example US, 2833
example USR, 2834
uniqueness
technique U, 2835
unit vectors
basis
theorem SUVB, 2836
definition SUV, 2837
orthogonal
example SUVOS, 2838
unitary
permutation matrix
example UPM, 2839
size 3
example UM3, 2840
unitary matrices
columns
theorem CUMOS, 2841
unitary matrix
inner product
theorem UMPIP, 2842
UPM (example), 2843
upper triangular matrix
definition UTM, 2844
US (example), 2845
USR (example), 2846
USR (theorem), 2847
UTM (definition), 2848
UTMR (subsection, section OD), 2849
UTMR (theorem), 2850
V (acronyms, section O), 2851
V (archetype), 2852
V (chapter), 2853
VA (example), 2854
Vandermonde matrix
definition VM, 2855
vandermonde matrix
determinant
theorem DVM, 2856
nonsingular
theorem NVM, 2857
size 4
example VM4, 2858
VEASM (subsection, section VO), 2859
vector
addition
definition CVA, 2860
column
definition CV, 2861
equality
definition CVE, 2862
notation, 2863
inner product
definition IP, 2864
norm
definition NV, 2865
notation, 2866
of constants
definition VOC, 2867
product with matrix, 2868, 2869
scalar multiplication
definition CVSM, 2870
vector addition
example VA, 2871
vector component
notation, 2872
vector form of solutions
Archetype D
example VFSAD, 2873
Archetype I
example VFSAI, 2874
Archetype L
example VFSAL, 2875
example VFS, 2876
mathematica, 2877
theorem VFSLS, 2878
vector linear combinations
mathematica, 2879
ti83, 2880
ti86, 2881
vector representation
example AVR, 2882
example VRC4, 2883
injective
theorem VRI, 2884
invertible
theorem VRILT, 2885
linear transformation
definition VR, 2886
notation, 2887
theorem VRLT, 2888
surjective
theorem VRS, 2889
theorem VRRB, 2890
vector representations
polynomials
example VRP2, 2891
vector scalar multiplication
example CVSM, 2892
vector space
characterization
theorem CFDVS, 2893
column vectors
definition VSCV, 2894
definition VS, 2895
infinite dimension
example VSPUD, 2896
linear transformations
theorem VSLT, 2897
over integers mod 5
example VSIM5, 2898
vector space of column vectors
notation, 2899
vector space of functions
example VSF, 2900
vector space of infinite sequences
example VSIS, 2901
vector space of matrices
definition VSM, 2902
example VSM, 2903
notation, 2904
vector space of polynomials
example VSP, 2905
vector space properties
column vectors
theorem VSPCV, 2906
matrices
theorem VSPM, 2907
vector space, crazy
example CVS, 2908
vector space, singleton
example VSS, 2909
vector spaces
isomorphic
definition IVS, 2910
theorem IFDVS, 2911
VESE (example), 2912
VFS (example), 2913
VFSAD (example), 2914
VFSAI (example), 2915
VFSAL (example), 2916
VFSLS (theorem), 2917
VFSS (subsection, section LC), 2918
VFSS.MMA (computation, section MMA), 2919
VLC.MMA (computation, section MMA), 2920
VLC.TI83 (computation, section TI83), 2921
VLC.TI86 (computation, section TI86), 2922
VM (definition), 2923
VM (section), 2924
VM4 (example), 2925
VO (section), 2926
VOC (definition), 2927
VR (definition), 2928
VR (notation), 2929
VR (section), 2930
VR (subsection, section LISS), 2931
VRC4 (example), 2932
VRI (theorem), 2933
VRILT (theorem), 2934
VRLT (theorem), 2935
VRP2 (example), 2936
VRRB (theorem), 2937
VRS (theorem), 2938
VS (acronyms, section PD), 2939
VS (chapter), 2940
VS (definition), 2941
VS (section), 2942
VS (subsection, section VS), 2943
VSCV (definition), 2944
VSCV (example), 2945
VSCV (notation), 2946
VSF (example), 2947
VSIM5 (example), 2948
VSIS (example), 2949
VSLT (theorem), 2950
VSM (definition), 2951
VSM (example), 2952
VSM (notation), 2953
VSP (example), 2954
VSP (subsection, section MO), 2955
VSP (subsection, section VO), 2956
VSP (subsection, section VS), 2957
VSPCV (theorem), 2958
VSPM (theorem), 2959
VSPUD (example), 2960
VSS (example), 2961
W (archetype), 2962
WILA (section), 2963
X (archetype), 2964
Z (Property), 2965
ZC (Property), 2966
ZCN (Property), 2967
ZCV (definition), 2968
ZCV (notation), 2969
zero
complex numbers
Property ZCN, 2970
field
Property ZF, 2971
zero column vector
definition ZCV, 2972
notation, 2973
zero matrix
notation, 2974
zero vector
column vectors
Property ZC, 2975
matrices
Property ZM, 2976
unique
theorem ZVU, 2977
vectors
Property Z, 2978
ZF (Property), 2979
ZM (definition), 2980
ZM (notation), 2981
ZM (Property), 2982
ZNDAB (example), 2983
ZSSM (theorem), 2984
ZVSM (theorem), 2985
ZVU (theorem), 2986