B (archetype), 98
B (definition), 99
B (section), 100
B (subsection, section B), 101
basis
columns nonsingular matrix
example CABAK, 102
common size
theorem BIS, 103
crazy vector apace
example BC, 104
definition B, 105
matrices
example BM, 106
example BSM22, 107
polynomials
example BP, 108
example BPR, 109
example BSP4, 110
example SVP4, 111
subspace of matrices
example BDM22, 112
BC (example), 113
BCS (theorem), 114
BDE (example), 115
BDM22 (example), 116
best cities
money magazine
example MBC, 117
BIS (theorem), 118
BM (example), 119
BNM (subsection, section B), 120
BNS (theorem), 121
BP (example), 122
BPR (example), 123
BRLT (example), 124
BRS (theorem), 125
BS (theorem), 126
BSCV (subsection, section B), 127
BSM22 (example), 128
BSP4 (example), 129
C (archetype), 130
C (definition), 131
C (notation), 132
C (part), 133
C (Property), 134
C (technique, section PT), 135
CABAK (example), 136
CACN (Property), 137
CAEHW (example), 138
CAF (Property), 139
canonical form
nilpotent linear transformation
example CFNLT, 140
theorem CFNLT, 141
CAV (subsection, section O), 142
Cayley-Hamilton
theorem CHT, 143
CB (section), 144
CB (theorem), 145
CBCV (example), 146
CBM (definition), 147
CBM (subsection, section CB), 148
CBP (example), 149
CC (Property), 150
CCCV (definition), 151
CCCV (notation), 152
CCM (definition), 153
CCM (example), 154
CCM (notation), 155
CCM (theorem), 156
CCN (definition), 157
CCN (notation), 158
CCN (subsection, section CNO), 159
CCRA (theorem), 160
CCRM (theorem), 161
CCS (subsection, section FS), 162
CCT (theorem), 163
CD (subsection, section DM), 164
CD (technique, section PT), 165
CEE (subsection, section EE), 166
CELT (example), 167
CELT (subsection, section CB), 168
CEMS6 (example), 169
CF (section), 170
CFDVS (theorem), 171
CFNLT (example), 172
CFNLT (subsection, section NLT), 173
CFNLT (theorem), 174
CFV (example), 175
change of basis
between polynomials
example CBP, 176
change-of-basis
between column vectors
example CBCV, 177
matrix representation
theorem MRCB, 178
similarity
theorem SCB, 179
theorem CB, 180
change-of-basis matrix
definition CBM, 181
inverse
theorem ICBM, 182
characteristic polynomial
definition CP, 183
degree
theorem DCP, 184
size 3 matrix
example CPMS3, 185
CHT (subsection, section JCF), 186
CHT (theorem), 187
CILT (subsection, section ILT), 188
CILTI (theorem), 189
CIM (subsection, section MISLE), 190
CINM (theorem), 191
CIVLT (example), 192
CIVLT (theorem), 193
CLI (theorem), 194
CLTLT (theorem), 195
CM (definition), 196
CM (Property), 197
CM32 (example), 198
CMCN (Property), 199
CMF (Property), 200
CMI (example), 201
CMIAB (example), 202
CMVEI (theorem), 203
CN (appendix), 204
CNA (definition), 205
CNA (notation), 206
CNA (subsection, section CNO), 207
CNE (definition), 208
CNE (notation), 209
CNM (definition), 210
CNM (notation), 211
CNMB (theorem), 212
CNO (section), 213
CNS1 (example), 214
CNS2 (example), 215
CNSV (example), 216
COB (theorem), 217
coefficient matrix
definition CM, 218
nonsingular
theorem SNCM, 219
column space
as null space
theorem FS, 220
Archetype A
example CSAA, 221
Archetype B
example CSAB, 222
as null space
example CSANS, 223
as null space, Archetype G
example FSAG, 224
as row space
theorem CSRST, 225
basis
theorem BCS, 226
consistent system
theorem CSCS, 227
consistent systems
example CSMCS, 228
isomorphic to range, 229
matrix, 230
nonsingular matrix
theorem CSNM, 231
notation, 232
original columns, Archetype D
example CSOCD, 233
row operations, Archetype I
example CSROI, 234
subspace
theorem CSMS, 235
testing membership
example MCSM, 236
two computations
example CSTW, 237
column vector addition
notation, 238
column vector scalar multiplication
notation, 239
commutativity
column vectors
Property CC, 240
matrices
Property CM, 241
vectors
Property C, 242
complex m-space
example VSCV, 243
complex arithmetic
example ACN, 244
complex number
conjugate
example CSCN, 245
modulus
example MSCN, 246
complex number
conjugate
definition CCN, 247
modulus
definition MCN, 248
complex numbers
addition
definition CNA, 249
notation, 250
arithmetic properties
theorem PCNA, 251
equality
definition CNE, 252
notation, 253
multiplication
definition CNM, 254
notation, 255
complex vector space
dimension
theorem DCM, 256
composition
injective linear transformations
theorem CILTI, 257
surjective linear transformations
theorem CSLTS, 258
conjugate
addition
theorem CCRA, 259
column vector
definition CCCV, 260
matrix
definition CCM, 261
notation, 262
multiplication
theorem CCRM, 263
notation, 264
of conjugate of a matrix
theorem CCM, 265
scalar multiplication
theorem CRSM, 266
twice
theorem CCT, 267
vector addition
theorem CRVA, 268
conjugate of a vector
notation, 269
conjugation
matrix addition
theorem CRMA, 270
matrix scalar multiplication
theorem CRMSM, 271
matrix transpose
theorem MCT, 272
consistent linear system, 273
consistent linear systems
theorem CSRN, 274
consistent system
definition CS, 275
constructive proofs
technique C, 276
contradiction
technique CD, 277
contrapositive
technique CP, 278
converse
technique CV, 279
coordinates
orthonormal basis
theorem COB, 280
coordinatization
linear combination of matrices
example CM32, 281
linear independence
theorem CLI, 282
orthonormal basis
example CROB3, 283
example CROB4, 284
spanning sets
theorem CSS, 285
coordinatization principle, 286
coordinatizing
polynomials
example CP2, 287
COV (example), 288
COV (subsection, section LDS), 289
CP (definition), 290
CP (subsection, section VR), 291
CP (technique, section PT), 292
CP2 (example), 293
CPMS3 (example), 294
CPSM (theorem), 295
crazy vector space
example CVSR, 296
properties
example PCVS, 297
CRMA (theorem), 298
CRMSM (theorem), 299
CRN (theorem), 300
CROB3 (example), 301
CROB4 (example), 302
CRS (section), 303
CRSM (theorem), 304
CRVA (theorem), 305
CS (definition), 306
CS (example), 307
CS (subsection, section TSS), 308
CSAA (example), 309
CSAB (example), 310
CSANS (example), 311
CSCN (example), 312
CSCS (theorem), 313
CSIP (example), 314
CSLT (subsection, section SLT), 315
CSLTS (theorem), 316
CSM (definition), 317
CSM (notation), 318
CSMCS (example), 319
CSMS (theorem), 320
CSNM (subsection, section CRS), 321
CSNM (theorem), 322
CSOCD (example), 323
CSRN (theorem), 324
CSROI (example), 325
CSRST (diagram), 326
CSRST (theorem), 327
CSS (theorem), 328
CSSE (subsection, section CRS), 329
CSSOC (subsection, section CRS), 330
CSTW (example), 331
CTD (subsection, section TD), 332
CTLT (example), 333
CUMOS (theorem), 334
curve fitting
polynomial through 5 points
example PTFP, 335
CV (definition), 336
CV (notation), 337
CV (technique, section PT), 338
CVA (definition), 339
CVA (notation), 340
CVC (notation), 341
CVE (definition), 342
CVE (notation), 343
CVS (example), 344
CVS (subsection, section VR), 345
CVSM (definition), 346
CVSM (example), 347
CVSM (notation), 348
CVSR (example), 349
D (archetype), 350
D (chapter), 351
D (definition), 352
D (notation), 353
D (section), 354
D (subsection, section D), 355
D (subsection, section SD), 356
D (technique, section PT), 357
D33M (example), 358
DAB (example), 359
DC (example), 360
DC (technique, section PT), 361
DC (theorem), 362
DCM (theorem), 363
DCN (Property), 364
DCP (theorem), 365
DD (subsection, section DM), 366
DEC (theorem), 367
decomposition
technique DC, 368
DED (theorem), 369
definition
A, 370
AM, 371
AME, 372
B, 373
C, 374
CBM, 375
CCCV, 376
CCM, 377
CCN, 378
CM, 379
CNA, 380
CNE, 381
CNM, 382
CP, 383
CS, 384
CSM, 385
CV, 386
CVA, 387
CVE, 388
CVSM, 389
D, 390
DIM, 391
DM, 392
DS, 393
DZM, 394
EEF, 395
EELT, 396
EEM, 397
ELEM, 398
EM, 399
EO, 400
ES, 401
ESYS, 402
F, 403
GES, 404
GEV, 405
GME, 406
HI, 407
HID, 408
HM, 409
HP, 410
HS, 411
IDLT, 412
IDV, 413
IE, 414
ILT, 415
IM, 416
IMP, 417
IP, 418
IS, 419
IVLT, 420
IVS, 421
JB, 422
JCF, 423
KLT, 424
LC, 425
LCCV, 426
LI, 427
LICV, 428
LNS, 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
MRLS, 444
MSM, 445
MVP, 446
NLT, 447
NM, 448
NOLT, 449
NOM, 450
NRML, 451
NSM, 452
NV, 453
ONS, 454
OSV, 455
OV, 456
PI, 457
PSM, 458
REM, 459
RLD, 460
RLDCV, 461
RLT, 462
RO, 463
ROLT, 464
ROM, 465
RR, 466
RREF, 467
RSM, 468
S, 469
SC, 470
SE, 471
SET, 472
SI, 473
SIM, 474
SLE, 475
SLT, 476
SM, 477
SOLV, 478
SQM, 479
SRM, 480
SS, 481
SSCV, 482
SSET, 483
SSLE, 484
SSSLE, 485
SU, 486
SUV, 487
SV, 488
SYM, 489
T, 490
technique D, 491
TM, 492
TS, 493
TSHSE, 494
TSVS, 495
UM, 496
UTM, 497
VM, 498
VOC, 499
VR, 500
VS, 501
VSCV, 502
VSM, 503
ZCV, 504
ZM, 505
DEHD (example), 506
DEM (theorem), 507
DEMMM (theorem), 508
DEMS5 (example), 509
DER (theorem), 510
DERC (theorem), 511
determinant
computed two ways
example TCSD, 512
definition DM, 513
equal rows or columns
theorem DERC, 514
expansion, columns
theorem DEC, 515
expansion, rows
theorem DER, 516
identity matrix
theorem DIM, 517
matrix multiplication
theorem DRMM, 518
nonsingular matrix, 519
notation, 520
row or column multiple
theorem DRCM, 521
row or column swap
theorem DRCS, 522
size 2 matrix
theorem DMST, 523
size 3 matrix
example D33M, 524
transpose
theorem DT, 525
via row operations
example DRO, 526
zero
theorem SMZD, 527
zero row or column
theorem DZRC, 528
zero versus nonzero
example ZNDAB, 529
determinant, upper triangular matrix
example DUTM, 530
determinants
elementary matrices
theorem DEMMM, 531
DF (Property), 532
DF (subsection, section CF), 533
DFS (subsection, section PD), 534
DFS (theorem), 535
DGES (theorem), 536
diagonal matrix
definition DIM, 537
diagonalizable
definition DZM, 538
distinct eigenvalues
example DEHD, 539
theorem DED, 540
full eigenspaces
theorem DMFE, 541
not
example NDMS4, 542
diagonalizable matrix
high power
example HPDM, 543
diagonalization
Archetype B
example DAB, 544
criteria
theorem DC, 545
example DMS3, 546
diagram
CSRST, 547
DLTA, 548
DLTM, 549
DTSLS, 550
FTMR, 551
FTMRA, 552
GLT, 553
ILT, 554
MRCLT, 555
NILT, 556
DIM (definition), 557
DIM (theorem), 558
dimension
crazy vector space
example DC, 559
definition D, 560
notation, 561
polynomial subspace
example DSP4, 562
proper subspaces
theorem PSSD, 563
subspace
example DSM22, 564
direct sum
decomposing zero vector
theorem DSZV, 565
definition DS, 566
dimension
theorem DSD, 567
example SDS, 568
from a basis
theorem DSFB, 569
from one subspace
theorem DSFOS, 570
notation, 571
zero intersection
theorem DSZI, 572
direct sums
linear independence
theorem DSLI, 573
repeated
theorem RDS, 574
distributivity
complex numbers
Property DCN, 575
field
Property DF, 576
distributivity, matrix addition
matrices
Property DMAM, 577
distributivity, scalar addition
column vectors
Property DSAC, 578
matrices
Property DSAM, 579
vectors
Property DSA, 580
distributivity, vector addition
column vectors
Property DVAC, 581
vectors
Property DVA, 582
DLDS (theorem), 583
DLTA (diagram), 584
DLTM (diagram), 585
DM (definition), 586
DM (notation), 587
DM (section), 588
DM (theorem), 589
DMAM (Property), 590
DMFE (theorem), 591
DMHP (subsection, section HP), 592
DMHP (theorem), 593
DMMP (theorem), 594
DMS3 (example), 595
DMST (theorem), 596
DNLT (theorem), 597
DNMMM (subsection, section PDM), 598
DP (theorem), 599
DRCM (theorem), 600
DRCMA (theorem), 601
DRCS (theorem), 602
DRMM (theorem), 603
DRO (example), 604
DRO (subsection, section PDM), 605
DROEM (subsection, section PDM), 606
DS (definition), 607
DS (notation), 608
DS (subsection, section PD), 609
DSA (Property), 610
DSAC (Property), 611
DSAM (Property), 612
DSD (theorem), 613
DSFB (theorem), 614
DSFOS (theorem), 615
DSLI (theorem), 616
DSM22 (example), 617
DSP4 (example), 618
DSZI (theorem), 619
DSZV (theorem), 620
DT (theorem), 621
DTSLS (diagram), 622
DUTM (example), 623
DVA (Property), 624
DVAC (Property), 625
DVM (theorem), 626
DVS (subsection, section D), 627
DZM (definition), 628
DZRC (theorem), 629
E (archetype), 630
E (chapter), 631
E (technique, section PT), 632
E.SAGE (computation, section SAGE), 633
ECEE (subsection, section EE), 634
EDELI (theorem), 635
EDYES (theorem), 636
EE (section), 637
EEE (subsection, section EE), 638
EEF (definition), 639
EEF (subsection, section FS), 640
EELT (definition), 641
EELT (subsection, section CB), 642
EEM (definition), 643
EEM (subsection, section EE), 644
EEMAP (theorem), 645
EENS (example), 646
EER (theorem), 647
EESR (theorem), 648
EHM (subsection, section PEE), 649
eigenspace
as null space
theorem EMNS, 650
definition EM, 651
invariant subspace
theorem EIS, 652
subspace
theorem EMS, 653
eigenspaces
sage, 654
eigenvalue
algebraic multiplicity
definition AME, 655
notation, 656
complex
example CEMS6, 657
definition EEM, 658
existence
example CAEHW, 659
theorem EMHE, 660
geometric multiplicity
definition GME, 661
notation, 662
index, 663
linear transformation
definition EELT, 664
multiplicities
example EMMS4, 665
power
theorem EOMP, 666
root of characteristic polynomial
theorem EMRCP, 667
scalar multiple
theorem ESMM, 668
symmetric matrix
example ESMS4, 669
zero
theorem SMZE, 670
eigenvalues
building desired
example BDE, 671
complex, of a linear transformation
example CELT, 672
conjugate pairs
theorem ERMCP, 673
distinct
example DEMS5, 674
example SEE, 675
Hermitian matrices
theorem HMRE, 676
inverse
theorem EIM, 677
maximum number
theorem MNEM, 678
multiplicities
example HMEM5, 679
theorem ME, 680
number
theorem NEM, 681
of a polynomial
theorem EPM, 682
size 3 matrix
example EMS3, 683
example ESMS3, 684
transpose
theorem ETM, 685
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 686
eigenvector, 687
linear transformation, 688
eigenvectors, 689
conjugate pairs, 690
Hermitian matrices
theorem HMOE, 691
linear transformation
example ELTBM, 692
example ELTBP, 693
linearly independent
theorem EDELI, 694
of a linear transformation
example ELTT, 695
EILT (subsection, section ILT), 696
EIM (theorem), 697
EIS (example), 698
EIS (theorem), 699
ELEM (definition), 700
ELEM (notation), 701
elementary matrices
definition ELEM, 702
determinants
theorem DEM, 703
nonsingular
theorem EMN, 704
notation, 705
row operations
example EMRO, 706
theorem EMDRO, 707
ELIS (theorem), 708
ELTBM (example), 709
ELTBP (example), 710
ELTT (example), 711
EM (definition), 712
EM (subsection, section DM), 713
EMDRO (theorem), 714
EMHE (theorem), 715
EMMS4 (example), 716
EMMVP (theorem), 717
EMN (theorem), 718
EMNS (theorem), 719
EMP (theorem), 720
empty set, 721
notation, 722
EMRCP (theorem), 723
EMRO (example), 724
EMS (theorem), 725
EMS3 (example), 726
ENLT (theorem), 727
EO (definition), 728
EOMP (theorem), 729
EOPSS (theorem), 730
EPM (theorem), 731
EPSM (theorem), 732
equal matrices
via equal matrix-vector products
theorem EMMVP, 733
equation operations
definition EO, 734
theorem EOPSS, 735
equivalence statements
technique E, 736
equivalences
technique ME, 737
equivalent systems
definition ESYS, 738
ERMCP (theorem), 739
ES (definition), 740
ES (notation), 741
ESEO (subsection, section SSLE), 742
ESLT (subsection, section SLT), 743
ESMM (theorem), 744
ESMS3 (example), 745
ESMS4 (example), 746
ESYS (definition), 747
ETM (theorem), 748
EVS (subsection, section VS), 749
example
AALC, 750
ABLC, 751
ABS, 752
ACN, 753
AHSAC, 754
AIVLT, 755
ALT, 756
ALTMM, 757
AM, 758
AMAA, 759
ANILT, 760
ANM, 761
AOS, 762
ASC, 763
AVR, 764
BC, 765
BDE, 766
BDM22, 767
BM, 768
BP, 769
BPR, 770
BRLT, 771
BSM22, 772
BSP4, 773
CABAK, 774
CAEHW, 775
CBCV, 776
CBP, 777
CCM, 778
CELT, 779
CEMS6, 780
CFNLT, 781
CFV, 782
CIVLT, 783
CM32, 784
CMI, 785
CMIAB, 786
CNS1, 787
CNS2, 788
CNSV, 789
COV, 790
CP2, 791
CPMS3, 792
CROB3, 793
CROB4, 794
CS, 795
CSAA, 796
CSAB, 797
CSANS, 798
CSCN, 799
CSIP, 800
CSMCS, 801
CSOCD, 802
CSROI, 803
CSTW, 804
CTLT, 805
CVS, 806
CVSM, 807
CVSR, 808
D33M, 809
DAB, 810
DC, 811
DEHD, 812
DEMS5, 813
DMS3, 814
DRO, 815
DSM22, 816
DSP4, 817
DUTM, 818
EENS, 819
EIS, 820
ELTBM, 821
ELTBP, 822
ELTT, 823
EMMS4, 824
EMRO, 825
EMS3, 826
ESMS3, 827
ESMS4, 828
FDV, 829
FF8, 830
FRAN, 831
FS1, 832
FS2, 833
FSAG, 834
FSCF, 835
GE4, 836
GE6, 837
GENR6, 838
GSTV, 839
HISAA, 840
HISAD, 841
HMEM5, 842
HP, 843
HPDM, 844
HUSAB, 845
IAP, 846
IAR, 847
IAS, 848
IAV, 849
ILTVR, 850
IM, 851
IM11, 852
IS, 853
ISJB, 854
ISMR4, 855
ISMR6, 856
ISSI, 857
IVSAV, 858
JB4, 859
JCF10, 860
KPNLT, 861
KVMR, 862
LCM, 863
LDCAA, 864
LDHS, 865
LDP4, 866
LDRN, 867
LDS, 868
LIC, 869
LICAB, 870
LIHS, 871
LIM32, 872
LINSB, 873
LIP4, 874
LIS, 875
LLDS, 876
LNS, 877
LTDB1, 878
LTDB2, 879
LTDB3, 880
LTM, 881
LTPM, 882
LTPP, 883
LTRGE, 884
MA, 885
MBC, 886
MCSM, 887
MFLT, 888
MI, 889
MIVS, 890
MMNC, 891
MNSLE, 892
MOLT, 893
MPMR, 894
MRBE, 895
MRCM, 896
MSCN, 897
MSM, 898
MTV, 899
MWIAA, 900
NDMS4, 901
NIAO, 902
NIAQ, 903
NIAQR, 904
NIDAU, 905
NJB5, 906
NKAO, 907
NLT, 908
NM, 909
NM62, 910
NM64, 911
NM83, 912
NRREF, 913
NSAO, 914
NSAQ, 915
NSAQR, 916
NSC2A, 917
NSC2S, 918
NSC2Z, 919
NSDAT, 920
NSDS, 921
NSE, 922
NSEAI, 923
NSLE, 924
NSLIL, 925
NSNM, 926
NSR, 927
NSS, 928
OLTTR, 929
ONFV, 930
ONTV, 931
OSGMD, 932
OSMC, 933
PCVS, 934
PM, 935
PSHS, 936
PTFP, 937
PTM, 938
PTMEE, 939
RAO, 940
RES, 941
RNM, 942
RNSM, 943
ROD2, 944
ROD4, 945
RREF, 946
RREFN, 947
RRTI, 948
RS, 949
RSAI, 950
RSB, 951
RSC4, 952
RSC5, 953
RSNS, 954
RSREM, 955
RVMR, 956
S, 957
SAA, 958
SAB, 959
SABMI, 960
SAE, 961
SAN, 962
SAR, 963
SAV, 964
SC, 965
SC3, 966
SCAA, 967
SCAB, 968
SCAD, 969
SDS, 970
SEE, 971
SEEF, 972
SETM, 973
SI, 974
SM2Z7, 975
SM32, 976
SMLT, 977
SMS3, 978
SMS5, 979
SP4, 980
SPIAS, 981
SRR, 982
SS, 983
SS6W, 984
SSC, 985
SSET, 986
SSM22, 987
SSNS, 988
SSP, 989
SSP4, 990
STLT, 991
STNE, 992
SU, 993
SUVOS, 994
SVP4, 995
SYM, 996
TCSD, 997
TD4, 998
TDEE6, 999
TDSSE, 1000
TIS, 1001
TIVS, 1002
TKAP, 1003
TLC, 1004
TM, 1005
TMP, 1006
TOV, 1007
TREM, 1008
TTS, 1009
UM3, 1010
UPM, 1011
US, 1012
USR, 1013
VA, 1014
VESE, 1015
VFS, 1016
VFSAD, 1017
VFSAI, 1018
VFSAL, 1019
VM4, 1020
VRC4, 1021
VRP2, 1022
VSCV, 1023
VSF, 1024
VSIM5, 1025
VSIS, 1026
VSM, 1027
VSP, 1028
VSPUD, 1029
VSS, 1030
ZNDAB, 1031
EXC (subsection, section B), 1032
EXC (subsection, section CB), 1033
EXC (subsection, section CF), 1034
EXC (subsection, section CRS), 1035
EXC (subsection, section D), 1036
EXC (subsection, section DM), 1037
EXC (subsection, section EE), 1038
EXC (subsection, section F), 1039
EXC (subsection, section FS), 1040
EXC (subsection, section HP), 1041
EXC (subsection, section HSE), 1042
EXC (subsection, section ILT), 1043
EXC (subsection, section IS), 1044
EXC (subsection, section IVLT), 1045
EXC (subsection, section LC), 1046
EXC (subsection, section LDS), 1047
EXC (subsection, section LI), 1048
EXC (subsection, section LISS), 1049
EXC (subsection, section LT), 1050
EXC (subsection, section MINM), 1051
EXC (subsection, section MISLE), 1052
EXC (subsection, section MM), 1053
EXC (subsection, section MO), 1054
EXC (subsection, section MR), 1055
EXC (subsection, section NM), 1056
EXC (subsection, section O), 1057
EXC (subsection, section PD), 1058
EXC (subsection, section PDM), 1059
EXC (subsection, section PEE), 1060
EXC (subsection, section PSM), 1061
EXC (subsection, section RREF), 1062
EXC (subsection, section S), 1063
EXC (subsection, section SD), 1064
EXC (subsection, section SLT), 1065
EXC (subsection, section SS), 1066
EXC (subsection, section SSLE), 1067
EXC (subsection, section T), 1068
EXC (subsection, section TSS), 1069
EXC (subsection, section VO), 1070
EXC (subsection, section VR), 1071
EXC (subsection, section VS), 1072
EXC (subsection, section WILA), 1073
extended echelon form
submatrices
example SEEF, 1074
extended reduced row-echelon form
properties
theorem PEEF, 1075
F (archetype), 1076
F (definition), 1077
F (section), 1078
F (subsection, section F), 1079
FDV (example), 1080
FF (subsection, section F), 1081
FF8 (example), 1082
Fibonacci sequence
example FSCF, 1083
field
definition F, 1084
FIMP (theorem), 1085
finite field
size 8
example FF8, 1086
four subsets
example FS1, 1087
example FS2, 1088
four subspaces
dimension
theorem DFS, 1089
FRAN (example), 1090
free variables
example CFV, 1091
free variables, number
theorem FVCS, 1092
free, independent variables
example FDV, 1093
FS (section), 1094
FS (subsection, section FS), 1095
FS (subsection, section SD), 1096
FS (theorem), 1097
FS1 (example), 1098
FS2 (example), 1099
FSAG (example), 1100
FSCF (example), 1101
FTMR (diagram), 1102
FTMR (theorem), 1103
FTMRA (diagram), 1104
FV (subsection, section TSS), 1105
FVCS (theorem), 1106
G (archetype), 1107
G (theorem), 1108
GE4 (example), 1109
GE6 (example), 1110
GEE (subsection, section IS), 1111
GEK (theorem), 1112
generalized eigenspace
as kernel
theorem GEK, 1113
definition GES, 1114
dimension
theorem DGES, 1115
dimension 4 domain
example GE4, 1116
dimension 6 domain
example GE6, 1117
invariant subspace
theorem GESIS, 1118
nilpotent restriction
theorem RGEN, 1119
nilpotent restrictions, dimension 6 domain
example GENR6, 1120
notation, 1121
generalized eigenspace decomposition
theorem GESD, 1122
generalized eigenvector
definition GEV, 1123
GENR6 (example), 1124
GES (definition), 1125
GES (notation), 1126
GESD (subsection, section JCF), 1127
GESD (theorem), 1128
GESIS (theorem), 1129
GEV (definition), 1130
GFDL (appendix), 1131
GLT (diagram), 1132
GME (definition), 1133
GME (notation), 1134
goldilocks
theorem G, 1135
Gram-Schmidt
column vectors
theorem GSP, 1136
three vectors
example GSTV, 1137
gram-schmidt
mathematica, 1138
GS (technique, section PT), 1139
GSP (subsection, section O), 1140
GSP (theorem), 1141
GSP.MMA (computation, section MMA), 1142
GSTV (example), 1143
GT (subsection, section PD), 1144
H (archetype), 1145
Hadamard Identity
notation, 1146
Hadamard identity
definition HID, 1147
Hadamard Inverse
notation, 1148
Hadamard inverse
definition HI, 1149
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1150
notation, 1151
Hadamard product
commutativity
theorem HPC, 1152
definition HP, 1153
diagonal matrices
theorem DMMP, 1154
distributivity
theorem HPDAA, 1155
example HP, 1156
identity
theorem HPHID, 1157
inverse
theorem HPHI, 1158
scalar matrix multiplication
theorem HPSMM, 1159
hermitian
definition HM, 1160
Hermitian matrix
inner product
theorem HMIP, 1161
HI (definition), 1162
HI (notation), 1163
HID (definition), 1164
HID (notation), 1165
HISAA (example), 1166
HISAD (example), 1167
HM (definition), 1168
HM (subsection, section MM), 1169
HMEM5 (example), 1170
HMIP (theorem), 1171
HMOE (theorem), 1172
HMRE (theorem), 1173
HMVEI (theorem), 1174
homogeneous system
Archetype C
example AHSAC, 1175
consistent
theorem HSC, 1176
definition HS, 1177
infinitely many solutions
theorem HMVEI, 1178
homogeneous systems
linear independence, 1179
HP (definition), 1180
HP (example), 1181
HP (notation), 1182
HP (section), 1183
HPC (theorem), 1184
HPDAA (theorem), 1185
HPDM (example), 1186
HPHI (theorem), 1187
HPHID (theorem), 1188
HPSMM (theorem), 1189
HS (definition), 1190
HSC (theorem), 1191
HSE (section), 1192
HUSAB (example), 1193
I (archetype), 1194
I (technique, section PT), 1195
IAP (example), 1196
IAR (example), 1197
IAS (example), 1198
IAV (example), 1199
ICBM (theorem), 1200
ICLT (theorem), 1201
identities
technique PI, 1202
identity matrix
determinant, 1203
example IM, 1204
notation, 1205
IDLT (definition), 1206
IDV (definition), 1207
IE (definition), 1208
IE (notation), 1209
IFDVS (theorem), 1210
IILT (theorem), 1211
ILT (definition), 1212
ILT (diagram), 1213
ILT (section), 1214
ILTB (theorem), 1215
ILTD (subsection, section ILT), 1216
ILTD (theorem), 1217
ILTIS (theorem), 1218
ILTLI (subsection, section ILT), 1219
ILTLI (theorem), 1220
ILTLT (theorem), 1221
ILTVR (example), 1222
IM (definition), 1223
IM (example), 1224
IM (notation), 1225
IM (subsection, section MISLE), 1226
IM11 (example), 1227
IMILT (theorem), 1228
IMP (definition), 1229
IMR (theorem), 1230
inconsistent linear systems
theorem ISRN, 1231
independent, dependent variables
definition IDV, 1232
indesxstring
example SM2Z7, 1233
example SSET, 1234
index
eigenvalue
definition IE, 1235
notation, 1236
indexstring
theorem DRCMA, 1237
theorem OBUTR, 1238
theorem UMCOB, 1239
induction
technique I, 1240
infinite solution set
example ISSI, 1241
infinite solutions, 3 × 4
example IS, 1242
injective
example IAP, 1243
example IAR, 1244
not
example NIAO, 1245
example NIAQ, 1246
example NIAQR, 1247
not, by dimension
example NIDAU, 1248
polynomials to matrices
example IAV, 1249
injective linear transformation
bases
theorem ILTB, 1250
injective linear transformations
dimension
theorem ILTD, 1251
inner product
anti-commutative
theorem IPAC, 1252
example CSIP, 1253
norm
theorem IPN, 1254
notation, 1255
positive
theorem PIP, 1256
scalar multiplication
theorem IPSM, 1257
vector addition
theorem IPVA, 1258
integers
mod p
definition IMP, 1259
mod p, field
theorem FIMP, 1260
mod 11
example IM11, 1261
interpolating polynomial
theorem IP, 1262
invariant subspace
definition IS, 1263
eigenspace, 1264
eigenspaces
example EIS, 1265
example TIS, 1266
Jordan block
example ISJB, 1267
kernels of powers
theorem KPIS, 1268
inverse
composition of linear transformations
theorem ICLT, 1269
example CMI, 1270
example MI, 1271
notation, 1272
of a matrix, 1273
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1274
invertible linear transformations
composition
theorem CIVLT, 1275
computing
example CIVLT, 1276
IP (definition), 1277
IP (notation), 1278
IP (subsection, section O), 1279
IP (theorem), 1280
IPAC (theorem), 1281
IPN (theorem), 1282
IPSM (theorem), 1283
IPVA (theorem), 1284
IS (definition), 1285
IS (example), 1286
IS (section), 1287
IS (subsection, section IS), 1288
ISJB (example), 1289
ISMR4 (example), 1290
ISMR6 (example), 1291
isomorphic
multiple vector spaces
example MIVS, 1292
vector spaces
example IVSAV, 1293
isomorphic vector spaces
dimension
theorem IVSED, 1294
example TIVS, 1295
ISRN (theorem), 1296
ISSI (example), 1297
ITMT (theorem), 1298
IV (subsection, section IVLT), 1299
IVLT (definition), 1300
IVLT (section), 1301
IVLT (subsection, section IVLT), 1302
IVLT (subsection, section MR), 1303
IVS (definition), 1304
IVSAV (example), 1305
IVSED (theorem), 1306
J (archetype), 1307
JB (definition), 1308
JB (notation), 1309
JB4 (example), 1310
JCF (definition), 1311
JCF (section), 1312
JCF (subsection, section JCF), 1313
JCF10 (example), 1314
JCFLT (theorem), 1315
Jordan block
definition JB, 1316
nilpotent
theorem NJB, 1317
notation, 1318
size 4
example JB4, 1319
Jordan canonical form
definition JCF, 1320
size 10
example JCF10, 1321
K (archetype), 1322
kernel
injective linear transformation
theorem KILT, 1323
isomorphic to null space
theorem KNSI, 1324
linear transformation
example NKAO, 1325
notation, 1326
of a linear transformation
definition KLT, 1327
pre-image, 1328
subspace
theorem KLTS, 1329
trivial
example TKAP, 1330
via matrix representation
example KVMR, 1331
KILT (theorem), 1332
KLT (definition), 1333
KLT (notation), 1334
KLT (subsection, section ILT), 1335
KLTS (theorem), 1336
KNSI (theorem), 1337
KPI (theorem), 1338
KPIS (theorem), 1339
KPLT (theorem), 1340
KPNLT (example), 1341
KPNLT (theorem), 1342
KVMR (example), 1343
L (archetype), 1344
L (technique, section PT), 1345
LA (subsection, section WILA), 1346
LC (definition), 1347
LC (section), 1348
LC (subsection, section LC), 1349
LC (technique, section PT), 1350
LCCV (definition), 1351
LCM (example), 1352
LDCAA (example), 1353
LDHS (example), 1354
LDP4 (example), 1355
LDRN (example), 1356
LDS (example), 1357
LDS (section), 1358
LDSS (subsection, section LDS), 1359
least squares
minimizes residuals
theorem LSMR, 1360
least squares solution
definition LSS, 1361
left null space
as row space, 1362
definition LNS, 1363
example LNS, 1364
notation, 1365
subspace
theorem LNSMS, 1366
lemma
technique LC, 1367
LI (definition), 1368
LI (section), 1369
LI (subsection, section LISS), 1370
LIC (example), 1371
LICAB (example), 1372
LICV (definition), 1373
LIHS (example), 1374
LIM32 (example), 1375
linear combination
system of equations
example ABLC, 1376
definition LC, 1377
definition LCCV, 1378
example TLC, 1379
linear transformation, 1380
matrices
example LCM, 1381
system of equations
example AALC, 1382
linear combinations
solutions to linear systems
theorem SLSLC, 1383
linear dependence
more vectors than size
theorem MVSLD, 1384
linear independence
definition LI, 1385
definition LICV, 1386
homogeneous systems
theorem LIVHS, 1387
injective linear transformation
theorem ILTLI, 1388
matrices
example LIM32, 1389
orthogonal, 1390
r and n
theorem LIVRN, 1391
linear solve
mathematica, 1392
sage, 1393
linear system
consistent
theorem RCLS, 1394
matrix representation
definition MRLS, 1395
notation, 1396
linear systems
notation
example MNSLE, 1397
example NSLE, 1398
linear transformation
polynomials to polynomials
example LTPP, 1399
addition
definition LTA, 1400
theorem MLTLT, 1401
theorem SLTLT, 1402
as matrix multiplication
example ALTMM, 1403
basis of range
example BRLT, 1404
checking
example ALT, 1405
composition
definition LTC, 1406
theorem CLTLT, 1407
defined by a matrix
example LTM, 1408
defined on a basis
example LTDB1, 1409
example LTDB2, 1410
example LTDB3, 1411
theorem LTDB, 1412
definition LT, 1413
identity
definition IDLT, 1414
injection
definition ILT, 1415
inverse
theorem ILTLT, 1416
inverse of inverse
theorem IILT, 1417
invertible
definition IVLT, 1418
example AIVLT, 1419
invertible, injective and surjective
theorem ILTIS, 1420
Jordan canonical form
theorem JCFLT, 1421
kernels of powers
theorem KPLT, 1422
linear combination
theorem LTLC, 1423
matrix of, 1424
example MFLT, 1425
example MOLT, 1426
not
example NLT, 1427
not invertible
example ANILT, 1428
notation, 1429
polynomials to matrices
example LTPM, 1430
rank plus nullity
theorem RPNDD, 1431
restriction
definition LTR, 1432
notation, 1433
scalar multiple
example SMLT, 1434
scalar multiplication
definition LTSM, 1435
spanning range
theorem SSRLT, 1436
sum
example STLT, 1437
surjection
definition SLT, 1438
vector space of, 1439
zero vector
theorem LTTZZ, 1440
linear transformation inverse
via matrix representation
example ILTVR, 1441
linear transformation restriction
on generalized eigenspace
example LTRGE, 1442
linear transformations
compositions
example CTLT, 1443
from matrices
theorem MBLT, 1444
linearly dependent
r < n
example LDRN, 1445
via homogeneous system
example LDHS, 1446
linearly dependent columns
Archetype A
example LDCAA, 1447
linearly dependent set
example LDS, 1448
linear combinations within
theorem DLDS, 1449
polynomials
example LDP4, 1450
linearly independent
crazy vector space
example LIC, 1451
extending sets
theorem ELIS, 1452
polynomials
example LIP4, 1453
via homogeneous system
example LIHS, 1454
linearly independent columns
Archetype B
example LICAB, 1455
linearly independent set
example LIS, 1456
example LLDS, 1457
LINM (subsection, section LI), 1458
LINSB (example), 1459
LIP4 (example), 1460
LIS (example), 1461
LISS (section), 1462
LISV (subsection, section LI), 1463
LIVHS (theorem), 1464
LIVRN (theorem), 1465
LLDS (example), 1466
LNS (definition), 1467
LNS (example), 1468
LNS (notation), 1469
LNS (subsection, section FS), 1470
LNSMS (theorem), 1471
lower triangular matrix
definition LTM, 1472
LS.MMA (computation, section MMA), 1473
LS.SAGE (computation, section SAGE), 1474
LSMR (theorem), 1475
LSS (definition), 1476
LT (chapter), 1477
LT (definition), 1478
LT (notation), 1479
LT (section), 1480
LT (subsection, section LT), 1481
LTA (definition), 1482
LTC (definition), 1483
LTC (subsection, section LT), 1484
LTDB (theorem), 1485
LTDB1 (example), 1486
LTDB2 (example), 1487
LTDB3 (example), 1488
LTLC (subsection, section LT), 1489
LTLC (theorem), 1490
LTM (definition), 1491
LTM (example), 1492
LTPM (example), 1493
LTPP (example), 1494
LTR (definition), 1495
LTR (notation), 1496
LTRGE (example), 1497
LTSM (definition), 1498
LTTZZ (theorem), 1499
M (archetype), 1500
M (chapter), 1501
M (definition), 1502
M (notation), 1503
MA (definition), 1504
MA (example), 1505
MA (notation), 1506
MACN (Property), 1507
MAF (Property), 1508
MAP (subsection, section SVD), 1509
mathematica
gram-schmidt (computation), 1510
linear solve (computation), 1511
matrix entry (computation), 1512
matrix inverse (computation), 1513
matrix multiplication (computation), 1514
null space (computation), 1515
row reduce (computation), 1516
transpose of a matrix (computation), 1517
vector form of solutions (computation), 1518
vector linear combinations (computation), 1519
mathematical language
technique L, 1520
matrix
addition
definition MA, 1521
notation, 1522
augmented
definition AM, 1523
column space
definition CSM, 1524
complex conjugate
example CCM, 1525
definition M, 1526
equality
definition ME, 1527
notation, 1528
example AM, 1529
identity
definition IM, 1530
inverse
definition MI, 1531
nonsingular
definition NM, 1532
notation, 1533
of a linear transformation
theorem MLTCV, 1534
product
example PTM, 1535
example PTMEE, 1536
product with vector
definition MVP, 1537
rectangular, 1538
row space
definition RSM, 1539
scalar multiplication
definition MSM, 1540
notation, 1541
singular, 1542
square
definition SQM, 1543
submatrices
example SS, 1544
submatrix
definition SM, 1545
symmetric
definition SYM, 1546
transpose
definition TM, 1547
unitary
definition UM, 1548
unitary is invertible
theorem UMI, 1549
zero
definition ZM, 1550
matrix addition
example MA, 1551
matrix components
notation, 1552
matrix entry
mathematica, 1553
sage, 1554
ti83, 1555
ti86, 1556
matrix inverse
Archetype B, 1557
computation
theorem CINM, 1558
mathematica, 1559
nonsingular matrix
theorem NI, 1560
of a matrix inverse
theorem MIMI, 1561
one-sided
theorem OSIS, 1562
product
theorem SS, 1563
sage, 1564
scalar multiple
theorem MISM, 1565
size 2 matrices
theorem TTMI, 1566
transpose
theorem MIT, 1567
uniqueness
theorem MIU, 1568
matrix multiplication
adjoints
theorem MMAD, 1569
associativity
theorem MMA, 1570
complex conjugation
theorem MMCC, 1571
definition MM, 1572
distributivity
theorem MMDAA, 1573
entry-by-entry
theorem EMP, 1574
identity matrix
theorem MMIM, 1575
inner product
theorem MMIP, 1576
mathematica, 1577
noncommutative
example MMNC, 1578
scalar matrix multiplication
theorem MMSMM, 1579
systems of linear equations
theorem SLEMM, 1580
transposes
theorem MMT, 1581
zero matrix
theorem MMZM, 1582
matrix product
as composition of linear transformations
example MPMR, 1583
matrix representation
basis of eigenvectors
example MRBE, 1584
composition of linear transformations
theorem MRCLT, 1585
definition MR, 1586
invertible
theorem IMR, 1587
multiple of a linear transformation
theorem MRMLT, 1588
notation, 1589
restriction to generalized eigenspace
theorem MRRGE, 1590
sum of linear transformations
theorem MRSLT, 1591
theorem FTMR, 1592
upper triangular
theorem UTMR, 1593
matrix representations
converting with change-of-basis
example MRCM, 1594
example OLTTR, 1595
matrix scalar multiplication
example MSM, 1596
matrix vector space
dimension
theorem DM, 1597
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1598
matrix-vector product
example MTV, 1599
notation, 1600
MBC (example), 1601
MBLT (theorem), 1602
MC (notation), 1603
MCC (subsection, section MO), 1604
MCCN (Property), 1605
MCF (Property), 1606
MCN (definition), 1607
MCN (subsection, section CNO), 1608
MCSM (example), 1609
MCT (theorem), 1610
MD (chapter), 1611
ME (definition), 1612
ME (notation), 1613
ME (subsection, section PEE), 1614
ME (technique, section PT), 1615
ME (theorem), 1616
ME.MMA (computation, section MMA), 1617
ME.SAGE (computation, section SAGE), 1618
ME.TI83 (computation, section TI83), 1619
ME.TI86 (computation, section TI86), 1620
MEASM (subsection, section MO), 1621
MFLT (example), 1622
MI (definition), 1623
MI (example), 1624
MI (notation), 1625
MI.MMA (computation, section MMA), 1626
MI.SAGE (computation, section SAGE), 1627
MICN (Property), 1628
MIF (Property), 1629
MIMI (theorem), 1630
MINM (section), 1631
MISLE (section), 1632
MISM (theorem), 1633
MIT (theorem), 1634
MIU (theorem), 1635
MIVS (example), 1636
MLT (subsection, section LT), 1637
MLTCV (theorem), 1638
MLTLT (theorem), 1639
MM (definition), 1640
MM (section), 1641
MM (subsection, section MM), 1642
MM.MMA (computation, section MMA), 1643
MMA (section), 1644
MMA (theorem), 1645
MMAD (theorem), 1646
MMCC (theorem), 1647
MMDAA (theorem), 1648
MMEE (subsection, section MM), 1649
MMIM (theorem), 1650
MMIP (theorem), 1651
MMNC (example), 1652
MMSMM (theorem), 1653
MMT (theorem), 1654
MMZM (theorem), 1655
MNEM (theorem), 1656
MNSLE (example), 1657
MO (section), 1658
MOLT (example), 1659
more variables than equations
example OSGMD, 1660
theorem CMVEI, 1661
MPMR (example), 1662
MR (definition), 1663
MR (notation), 1664
MR (section), 1665
MRBE (example), 1666
MRCB (theorem), 1667
MRCLT (diagram), 1668
MRCLT (theorem), 1669
MRCM (example), 1670
MRLS (definition), 1671
MRLS (notation), 1672
MRMLT (theorem), 1673
MRRGE (theorem), 1674
MRS (subsection, section CB), 1675
MRSLT (theorem), 1676
MSCN (example), 1677
MSM (definition), 1678
MSM (example), 1679
MSM (notation), 1680
MTV (example), 1681
multiplicative associativity
complex numbers
Property MACN, 1682
multiplicative closure
complex numbers
Property MCCN, 1683
field
Property MCF, 1684
multiplicative commutativity
complex numbers
Property CMCN, 1685
multiplicative inverse
complex numbers
Property MICN, 1686
MVNSE (subsection, section RREF), 1687
MVP (definition), 1688
MVP (notation), 1689
MVP (subsection, section MM), 1690
MVSLD (theorem), 1691
MWIAA (example), 1692
N (archetype), 1693
N (subsection, section O), 1694
N (technique, section PT), 1695
NDMS4 (example), 1696
negation of statements
technique N, 1697
NEM (theorem), 1698
NI (theorem), 1699
NIAO (example), 1700
NIAQ (example), 1701
NIAQR (example), 1702
NIDAU (example), 1703
nilpotent
linear transformation
definition NLT, 1704
NILT (diagram), 1705
NJB (theorem), 1706
NJB5 (example), 1707
NKAO (example), 1708
NLT (definition), 1709
NLT (example), 1710
NLT (section), 1711
NLT (subsection, section NLT), 1712
NLTFO (subsection, section LT), 1713
NM (definition), 1714
NM (example), 1715
NM (section), 1716
NM (subsection, section NM), 1717
NM (subsection, section OD), 1718
NM62 (example), 1719
NM64 (example), 1720
NM83 (example), 1721
NME1 (theorem), 1722
NME2 (theorem), 1723
NME3 (theorem), 1724
NME4 (theorem), 1725
NME5 (theorem), 1726
NME6 (theorem), 1727
NME7 (theorem), 1728
NME8 (theorem), 1729
NME9 (theorem), 1730
NMI (subsection, section MINM), 1731
NMLIC (theorem), 1732
NMPEM (theorem), 1733
NMRRI (theorem), 1734
NMTNS (theorem), 1735
NMUS (theorem), 1736
NOILT (theorem), 1737
NOLT (definition), 1738
NOLT (notation), 1739
NOM (definition), 1740
NOM (notation), 1741
nonsingular
columns as basis
theorem CNMB, 1742
nonsingular matrices
linearly independent columns
theorem NMLIC, 1743
nonsingular matrix
Archetype B
example NM, 1744
column space, 1745
elementary matrices
theorem NMPEM, 1746
equivalences
theorem NME1, 1747
theorem NME2, 1748
theorem NME3, 1749
theorem NME4, 1750
theorem NME5, 1751
theorem NME6, 1752
theorem NME7, 1753
theorem NME8, 1754
theorem NME9, 1755
matrix inverse, 1756
null space
example NSNM, 1757
nullity, 1758
product of nonsingular matrices
theorem NPNT, 1759
rank
theorem RNNM, 1760
row-reduced
theorem NMRRI, 1761
trivial null space
theorem NMTNS, 1762
unique solutions
theorem NMUS, 1763
nonsingular matrix, row-reduced
example NSR, 1764
norm
example CNSV, 1765
inner product, 1766
notation, 1767
normal matrix
definition NRML, 1768
example ANM, 1769
orthonormal basis, 1770
notation
A, 1771
AM, 1772
AME, 1773
C, 1774
CCCV, 1775
CCM, 1776
CCN, 1777
CNA, 1778
CNE, 1779
CNM, 1780
CSM, 1781
CV, 1782
CVA, 1783
CVC, 1784
CVE, 1785
CVSM, 1786
D, 1787
DM, 1788
DS, 1789
ELEM, 1790
ES, 1791
GES, 1792
GME, 1793
HI, 1794
HID, 1795
HP, 1796
IE, 1797
IM, 1798
IP, 1799
JB, 1800
KLT, 1801
LNS, 1802
LT, 1803
LTR, 1804
M, 1805
MA, 1806
MC, 1807
ME, 1808
MI, 1809
MR, 1810
MRLS, 1811
MSM, 1812
MVP, 1813
NOLT, 1814
NOM, 1815
NSM, 1816
NV, 1817
RLT, 1818
RO, 1819
ROLT, 1820
ROM, 1821
RREFA, 1822
RSM, 1823
SC, 1824
SE, 1825
SETM, 1826
SI, 1827
SM, 1828
SRM, 1829
SSET, 1830
SSV, 1831
SU, 1832
SUV, 1833
T, 1834
TM, 1835
VR, 1836
VSCV, 1837
VSM, 1838
ZCV, 1839
ZM, 1840
notation for a linear system
example NSE, 1841
NPNT (theorem), 1842
NRFO (subsection, section MR), 1843
NRML (definition), 1844
NRREF (example), 1845
NS.MMA (computation, section MMA), 1846
NSAO (example), 1847
NSAQ (example), 1848
NSAQR (example), 1849
NSC2A (example), 1850
NSC2S (example), 1851
NSC2Z (example), 1852
NSDAT (example), 1853
NSDS (example), 1854
NSE (example), 1855
NSEAI (example), 1856
NSLE (example), 1857
NSLIL (example), 1858
NSM (definition), 1859
NSM (notation), 1860
NSM (subsection, section HSE), 1861
NSMS (theorem), 1862
NSNM (example), 1863
NSNM (subsection, section NM), 1864
NSR (example), 1865
NSS (example), 1866
NSSLI (subsection, section LI), 1867
Null space
as a span
example NSDS, 1868
null space
Archetype I
example NSEAI, 1869
basis
theorem BNS, 1870
computation
example CNS1, 1871
example CNS2, 1872
isomorphic to kernel, 1873
linearly independent basis
example LINSB, 1874
mathematica, 1875
matrix
definition NSM, 1876
nonsingular matrix, 1877
notation, 1878
singular matrix, 1879
spanning set
example SSNS, 1880
theorem SSNS, 1881
subspace
theorem NSMS, 1882
null space span, linearly independent
Archetype L
example NSLIL, 1883
nullity
computing, 1884
injective linear transformation
theorem NOILT, 1885
linear transformation
definition NOLT, 1886
matrix, 1887
definition NOM, 1888
notation, 1889, 1890
square matrix, 1891
NV (definition), 1892
NV (notation), 1893
NVM (theorem), 1894
O (archetype), 1895
O (Property), 1896
O (section), 1897
OBC (subsection, section B), 1898
OBNM (theorem), 1899
OBUTR (theorem), 1900
OC (Property), 1901
OCN (Property), 1902
OD (section), 1903
OD (subsection, section OD), 1904
OD (theorem), 1905
OF (Property), 1906
OLTTR (example), 1907
OM (Property), 1908
one
column vectors
Property OC, 1909
complex numbers
Property OCN, 1910
field
Property OF, 1911
matrices
Property OM, 1912
vectors
Property O, 1913
ONFV (example), 1914
ONS (definition), 1915
ONTV (example), 1916
orthogonal
linear independence
theorem OSLI, 1917
set
example AOS, 1918
set of vectors
definition OSV, 1919
vector pairs
definition OV, 1920
orthogonal vectors
example TOV, 1921
orthonormal
definition ONS, 1922
matrix columns
example OSMC, 1923
orthonormal basis
normal matrix
theorem OBNM, 1924
orthonormal diagonalization
theorem OD, 1925
orthonormal set
four vectors
example ONFV, 1926
three vectors
example ONTV, 1927
OSGMD (example), 1928
OSIS (theorem), 1929
OSLI (theorem), 1930
OSMC (example), 1931
OSV (definition), 1932
OV (definition), 1933
OV (subsection, section O), 1934
P (appendix), 1935
P (archetype), 1936
P (technique, section PT), 1937
particular solutions
example PSHS, 1938
PCNA (theorem), 1939
PCVS (example), 1940
PD (section), 1941
PDM (section), 1942
PDM (theorem), 1943
PEE (section), 1944
PEEF (theorem), 1945
PI (definition), 1946
PI (subsection, section LT), 1947
PI (technique, section PT), 1948
PIP (theorem), 1949
PM (example), 1950
PM (subsection, section EE), 1951
PMI (subsection, section MISLE), 1952
PMM (subsection, section MM), 1953
PMR (subsection, section MR), 1954
PNLT (subsection, section NLT), 1955
POD (section), 1956
polar decomposition
theorem PDM, 1957
polynomial
of a matrix
example PM, 1958
polynomial vector space
dimension
theorem DP, 1959
positive semi-definite
creating
theorem CPSM, 1960
positive semi-definite matrix
definition PSM, 1961
eigenvalues
theorem EPSM, 1962
practice
technique P, 1963
pre-image
definition PI, 1964
kernel
theorem KPI, 1965
pre-images
example SPIAS, 1966
principal axis theorem, 1967
product of triangular matrices
theorem PTMT, 1968
Property
AA, 1969
AAC, 1970
AACN, 1971
AAF, 1972
AAM, 1973
AC, 1974
ACC, 1975
ACCN, 1976
ACF, 1977
ACM, 1978
AI, 1979
AIC, 1980
AICN, 1981
AIF, 1982
AIM, 1983
C, 1984
CACN, 1985
CAF, 1986
CC, 1987
CM, 1988
CMCN, 1989
CMF, 1990
DCN, 1991
DF, 1992
DMAM, 1993
DSA, 1994
DSAC, 1995
DSAM, 1996
DVA, 1997
DVAC, 1998
MACN, 1999
MAF, 2000
MCCN, 2001
MCF, 2002
MICN, 2003
MIF, 2004
O, 2005
OC, 2006
OCN, 2007
OF, 2008
OM, 2009
SC, 2010
SCC, 2011
SCM, 2012
SMA, 2013
SMAC, 2014
SMAM, 2015
Z, 2016
ZC, 2017
ZCN, 2018
ZF, 2019
ZM, 2020
PSHS (example), 2021
PSHS (subsection, section LC), 2022
PSM (definition), 2023
PSM (section), 2024
PSM (subsection, section PSM), 2025
PSM (subsection, section SD), 2026
PSMSR (theorem), 2027
PSPHS (theorem), 2028
PSS (subsection, section SSLE), 2029
PSSD (theorem), 2030
PSSLS (theorem), 2031
PT (section), 2032
PTFP (example), 2033
PTM (example), 2034
PTMEE (example), 2035
PTMT (theorem), 2036
Q (archetype), 2037
R (archetype), 2038
R (chapter), 2039
R.SAGE (computation, section SAGE), 2040
range
full
example FRAN, 2041
isomorphic to column space
theorem RCSI, 2042
linear transformation
example RAO, 2043
notation, 2044
of a linear transformation
definition RLT, 2045
pre-image
theorem RPI, 2046
subspace
theorem RLTS, 2047
surjective linear transformation
theorem RSLT, 2048
via matrix representation
example RVMR, 2049
rank
computing
theorem CRN, 2050
linear transformation
definition ROLT, 2051
matrix
definition ROM, 2052
example RNM, 2053
notation, 2054, 2055
of transpose
example RRTI, 2056
square matrix
example RNSM, 2057
surjective linear transformation
theorem ROSLT, 2058
transpose
theorem RMRT, 2059
rank one decomposition
size 2
example ROD2, 2060
size 4
example ROD4, 2061
theorem ROD, 2062
rank+nullity
theorem RPNC, 2063
RAO (example), 2064
RCLS (theorem), 2065
RCSI (theorem), 2066
RD (subsection, section VS), 2067
RDS (theorem), 2068
READ (subsection, section B), 2069
READ (subsection, section CB), 2070
READ (subsection, section CRS), 2071
READ (subsection, section D), 2072
READ (subsection, section DM), 2073
READ (subsection, section EE), 2074
READ (subsection, section FS), 2075
READ (subsection, section HSE), 2076
READ (subsection, section ILT), 2077
READ (subsection, section IVLT), 2078
READ (subsection, section LC), 2079
READ (subsection, section LDS), 2080
READ (subsection, section LI), 2081
READ (subsection, section LISS), 2082
READ (subsection, section LT), 2083
READ (subsection, section MINM), 2084
READ (subsection, section MISLE), 2085
READ (subsection, section MM), 2086
READ (subsection, section MO), 2087
READ (subsection, section MR), 2088
READ (subsection, section NM), 2089
READ (subsection, section O), 2090
READ (subsection, section PD), 2091
READ (subsection, section PDM), 2092
READ (subsection, section PEE), 2093
READ (subsection, section RREF), 2094
READ (subsection, section S), 2095
READ (subsection, section SD), 2096
READ (subsection, section SLT), 2097
READ (subsection, section SS), 2098
READ (subsection, section SSLE), 2099
READ (subsection, section TSS), 2100
READ (subsection, section VO), 2101
READ (subsection, section VR), 2102
READ (subsection, section VS), 2103
READ (subsection, section WILA), 2104
reduced row-echelon form
analysis
notation, 2105
definition RREF, 2106
example NRREF, 2107
example RREF, 2108
extended
definition EEF, 2109
notation
example RREFN, 2110
unique
theorem RREFU, 2111
reducing a span
example RSC5, 2112
relation of linear dependence
definition RLD, 2113
definition RLDCV, 2114
REM (definition), 2115
REMEF (theorem), 2116
REMES (theorem), 2117
REMRS (theorem), 2118
RES (example), 2119
RGEN (theorem), 2120
rings
sage, 2121
RLD (definition), 2122
RLDCV (definition), 2123
RLT (definition), 2124
RLT (notation), 2125
RLT (subsection, section IS), 2126
RLT (subsection, section SLT), 2127
RLTS (theorem), 2128
RMRT (theorem), 2129
RNLT (subsection, section IVLT), 2130
RNM (example), 2131
RNM (subsection, section D), 2132
RNNM (subsection, section D), 2133
RNNM (theorem), 2134
RNSM (example), 2135
RO (definition), 2136
RO (notation), 2137
RO (subsection, section RREF), 2138
ROD (section), 2139
ROD (theorem), 2140
ROD2 (example), 2141
ROD4 (example), 2142
ROLT (definition), 2143
ROLT (notation), 2144
ROM (definition), 2145
ROM (notation), 2146
ROSLT (theorem), 2147
row operations
definition RO, 2148
elementary matrices, 2149, 2150
notation, 2151
row reduce
mathematica, 2152
sage, 2153
ti83, 2154
ti86, 2155
row space
Archetype I
example RSAI, 2156
as column space, 2157
basis
example RSB, 2158
theorem BRS, 2159
matrix, 2160
notation, 2161
row-equivalent matrices
theorem REMRS, 2162
subspace
theorem RSMS, 2163
row-equivalent matrices
definition REM, 2164
example TREM, 2165
row space, 2166
row spaces
example RSREM, 2167
theorem REMES, 2168
row-reduce
the verb
definition RR, 2169
row-reduced matrices
theorem REMEF, 2170
RPI (theorem), 2171
RPNC (theorem), 2172
RPNDD (theorem), 2173
RR (definition), 2174
RR.MMA (computation, section MMA), 2175
RR.SAGE (computation, section SAGE), 2176
RR.TI83 (computation, section TI83), 2177
RR.TI86 (computation, section TI86), 2178
RREF (definition), 2179
RREF (example), 2180
RREF (section), 2181
RREF (subsection, section RREF), 2182
RREFA (notation), 2183
RREFN (example), 2184
RREFU (theorem), 2185
RRTI (example), 2186
RS (example), 2187
RSAI (example), 2188
RSB (example), 2189
RSC4 (example), 2190
RSC5 (example), 2191
RSLT (theorem), 2192
RSM (definition), 2193
RSM (notation), 2194
RSM (subsection, section CRS), 2195
RSMS (theorem), 2196
RSNS (example), 2197
RSREM (example), 2198
RT (subsection, section PD), 2199
RVMR (example), 2200
S (archetype), 2201
S (definition), 2202
S (example), 2203
S (section), 2204
SAA (example), 2205
SAB (example), 2206
SABMI (example), 2207
SAE (example), 2208
sage
eigenspaces (computation), 2209
linear solve (computation), 2210
matrix entry (computation), 2211
matrix inverse (computation), 2212
rings (computation), 2213
row reduce (computation), 2214
transpose of a matrix (computation), 2215
vector linear combinations (computation), 2216
SAGE (section), 2217
SAN (example), 2218
SAR (example), 2219
SAS (section), 2220
SAV (example), 2221
SC (definition), 2222
SC (example), 2223
SC (notation), 2224
SC (Property), 2225
SC (subsection, section S), 2226
SC (subsection, section SET), 2227
SC3 (example), 2228
SCAA (example), 2229
SCAB (example), 2230
SCAD (example), 2231
scalar closure
column vectors
Property SCC, 2232
matrices
Property SCM, 2233
vectors
Property SC, 2234
scalar multiple
matrix inverse, 2235
scalar multiplication
zero scalar
theorem ZSSM, 2236
zero vector
theorem ZVSM, 2237
zero vector result
theorem SMEZV, 2238
scalar multiplication associativity
column vectors
Property SMAC, 2239
matrices
Property SMAM, 2240
vectors
Property SMA, 2241
SCB (theorem), 2242
SCC (Property), 2243
SCM (Property), 2244
SD (section), 2245
SDS (example), 2246
SE (definition), 2247
SE (notation), 2248
secret sharing
6 ways
example SS6W, 2249
SEE (example), 2250
SEEF (example), 2251
SER (theorem), 2252
set
cardinality
definition C, 2253
example CS, 2254
notation, 2255
complement
definition SC, 2256
example SC, 2257
notation, 2258
definition SET, 2259
empty
definition ES, 2260
equality
definition SE, 2261
notation, 2262
intersection
definition SI, 2263
example SI, 2264
notation, 2265
membership
example SETM, 2266
notation, 2267
size, 2268
subset, 2269
union
definition SU, 2270
example SU, 2271
notation, 2272
SET (definition), 2273
SET (section), 2274
SETM (example), 2275
SETM (notation), 2276
shoes, 2277
SHS (subsection, section HSE), 2278
SI (definition), 2279
SI (example), 2280
SI (notation), 2281
SI (subsection, section IVLT), 2282
SIM (definition), 2283
similar matrices
equal eigenvalues
example EENS, 2284
eual eigenvalues
theorem SMEE, 2285
example SMS3, 2286
example SMS5, 2287
similarity
definition SIM, 2288
equivalence relation
theorem SER, 2289
singular matrix
Archetype A
example S, 2290
null space
example NSS, 2291
singular matrix, row-reduced
example SRR, 2292
singular value decomposition
theorem SVD, 2293
singular values
definition SV, 2294
SLE (chapter), 2295
SLE (definition), 2296
SLE (subsection, section SSLE), 2297
SLELT (subsection, section IVLT), 2298
SLEMM (theorem), 2299
SLSLC (theorem), 2300
SLT (definition), 2301
SLT (section), 2302
SLTB (theorem), 2303
SLTD (subsection, section SLT), 2304
SLTD (theorem), 2305
SLTLT (theorem), 2306
SM (definition), 2307
SM (notation), 2308
SM (subsection, section SD), 2309
SM2Z7 (example), 2310
SM32 (example), 2311
SMA (Property), 2312
SMAC (Property), 2313
SMAM (Property), 2314
SMEE (theorem), 2315
SMEZV (theorem), 2316
SMLT (example), 2317
SMS (theorem), 2318
SMS3 (example), 2319
SMS5 (example), 2320
SMZD (theorem), 2321
SMZE (theorem), 2322
SNCM (theorem), 2323
SO (subsection, section SET), 2324
socks, 2325
SOL (subsection, section B), 2326
SOL (subsection, section CB), 2327
SOL (subsection, section CRS), 2328
SOL (subsection, section D), 2329
SOL (subsection, section DM), 2330
SOL (subsection, section EE), 2331
SOL (subsection, section F), 2332
SOL (subsection, section FS), 2333
SOL (subsection, section HSE), 2334
SOL (subsection, section ILT), 2335
SOL (subsection, section IVLT), 2336
SOL (subsection, section LC), 2337
SOL (subsection, section LDS), 2338
SOL (subsection, section LI), 2339
SOL (subsection, section LISS), 2340
SOL (subsection, section LT), 2341
SOL (subsection, section MINM), 2342
SOL (subsection, section MISLE), 2343
SOL (subsection, section MM), 2344
SOL (subsection, section MO), 2345
SOL (subsection, section MR), 2346
SOL (subsection, section NM), 2347
SOL (subsection, section O), 2348
SOL (subsection, section PD), 2349
SOL (subsection, section PDM), 2350
SOL (subsection, section PEE), 2351
SOL (subsection, section RREF), 2352
SOL (subsection, section S), 2353
SOL (subsection, section SD), 2354
SOL (subsection, section SLT), 2355
SOL (subsection, section SS), 2356
SOL (subsection, section SSLE), 2357
SOL (subsection, section T), 2358
SOL (subsection, section TSS), 2359
SOL (subsection, section VO), 2360
SOL (subsection, section VR), 2361
SOL (subsection, section VS), 2362
SOL (subsection, section WILA), 2363
solution set
Archetype A
example SAA, 2364
archetype E
example SAE, 2365
theorem PSPHS, 2366
solution set of a linear system
definition SSSLE, 2367
solution sets
possibilities
theorem PSSLS, 2368
solution to a linear system
definition SSLE, 2369
solution vector
definition SOLV, 2370
SOLV (definition), 2371
solving homogeneous system
Archetype A
example HISAA, 2372
Archetype B
example HUSAB, 2373
Archetype D
example HISAD, 2374
solving nonlinear equations
example STNE, 2375
SP4 (example), 2376
span
basic
example ABS, 2377
basis
theorem BS, 2378
definition SS, 2379
definition SSCV, 2380
improved
example IAS, 2381
notation, 2382
reducing
example RSC4, 2383
reduction
example RS, 2384
removing vectors
example COV, 2385
reworking elements
example RES, 2386
set of polynomials
example SSP, 2387
subspace
theorem SSS, 2388
span of columns
Archetype A
example SCAA, 2389
Archetype B
example SCAB, 2390
Archetype D
example SCAD, 2391
spanning set
crazy vector space
example SSC, 2392
definition TSVS, 2393
matrices
example SSM22, 2394
more vectors
theorem SSLD, 2395
polynomials
example SSP4, 2396
SPIAS (example), 2397
SQM (definition), 2398
square root
eigenvalues, eigenspaces
theorem EESR, 2399
matrix
definition SRM, 2400
notation, 2401
positive semi-definite matrix
theorem PSMSR, 2402
unique
theorem USR, 2403
SR (section), 2404
SRM (definition), 2405
SRM (notation), 2406
SRM (subsection, section SR), 2407
SRR (example), 2408
SS (definition), 2409
SS (example), 2410
SS (section), 2411
SS (subsection, section LISS), 2412
SS (theorem), 2413
SS6W (example), 2414
SSC (example), 2415
SSCV (definition), 2416
SSET (definition), 2417
SSET (example), 2418
SSET (notation), 2419
SSLD (theorem), 2420
SSLE (definition), 2421
SSLE (section), 2422
SSM22 (example), 2423
SSNS (example), 2424
SSNS (subsection, section SS), 2425
SSNS (theorem), 2426
SSP (example), 2427
SSP4 (example), 2428
SSRLT (theorem), 2429
SSS (theorem), 2430
SSSLE (definition), 2431
SSSLT (subsection, section SLT), 2432
SSV (notation), 2433
SSV (subsection, section SS), 2434
standard unit vector
notation, 2435
starting proofs
technique GS, 2436
STLT (example), 2437
STNE (example), 2438
SU (definition), 2439
SU (example), 2440
SU (notation), 2441
submatrix
notation, 2442
subset
definition SSET, 2443
notation, 2444
subspace
as null space
example RSNS, 2445
characterized
example ASC, 2446
definition S, 2447
in {P}_{4}
example SP4, 2448
not, additive closure
example NSC2A, 2449
not, scalar closure
example NSC2S, 2450
not, zero vector
example NSC2Z, 2451
testing
theorem TSS, 2452
trivial
definition TS, 2453
verification
example SC3, 2454
example SM32, 2455
subspaces
equal dimension
theorem EDYES, 2456
surjective
Archetype N
example SAN, 2457
example SAR, 2458
not
example NSAQ, 2459
example NSAQR, 2460
not, Archetype O
example NSAO, 2461
not, by dimension
example NSDAT, 2462
polynomials to matrices
example SAV, 2463
surjective linear transformation
bases
theorem SLTB, 2464
surjective linear transformations
dimension
theorem SLTD, 2465
SUV (definition), 2466
SUV (notation), 2467
SUVB (theorem), 2468
SUVOS (example), 2469
SV (definition), 2470
SVD (section), 2471
SVD (subsection, section SVD), 2472
SVD (theorem), 2473
SVP4 (example), 2474
SYM (definition), 2475
SYM (example), 2476
symmetric matrices
theorem SMS, 2477
symmetric matrix
example SYM, 2478
system of equations
vector equality
example VESE, 2479
system of linear equations
definition SLE, 2480
T (archetype), 2481
T (definition), 2482
T (notation), 2483
T (part), 2484
T (section), 2485
T (technique, section PT), 2486
TCSD (example), 2487
TD (section), 2488
TD (subsection, section TD), 2489
TD (theorem), 2490
TD4 (example), 2491
TDEE (theorem), 2492
TDEE6 (example), 2493
TDSSE (example), 2494
TDSSE (subsection, section TD), 2495
technique
C, 2496
CD, 2497
CP, 2498
CV, 2499
D, 2500
DC, 2501
E, 2502
GS, 2503
I, 2504
L, 2505
LC, 2506
ME, 2507
N, 2508
P, 2509
PI, 2510
T, 2511
U, 2512
theorem
AA, 2513
AIP, 2514
AISM, 2515
AIU, 2516
AMA, 2517
AMSM, 2518
BCS, 2519
BIS, 2520
BNS, 2521
BRS, 2522
BS, 2523
CB, 2524
CCM, 2525
CCRA, 2526
CCRM, 2527
CCT, 2528
CFDVS, 2529
CFNLT, 2530
CHT, 2531
CILTI, 2532
CINM, 2533
CIVLT, 2534
CLI, 2535
CLTLT, 2536
CMVEI, 2537
CNMB, 2538
COB, 2539
CPSM, 2540
CRMA, 2541
CRMSM, 2542
CRN, 2543
CRSM, 2544
CRVA, 2545
CSCS, 2546
CSLTS, 2547
CSMS, 2548
CSNM, 2549
CSRN, 2550
CSRST, 2551
CSS, 2552
CUMOS, 2553
DC, 2554
DCM, 2555
DCP, 2556
DEC, 2557
DED, 2558
DEM, 2559
DEMMM, 2560
DER, 2561
DERC, 2562
DFS, 2563
DGES, 2564
DIM, 2565
DLDS, 2566
DM, 2567
DMFE, 2568
DMHP, 2569
DMMP, 2570
DMST, 2571
DNLT, 2572
DP, 2573
DRCM, 2574
DRCMA, 2575
DRCS, 2576
DRMM, 2577
DSD, 2578
DSFB, 2579
DSFOS, 2580
DSLI, 2581
DSZI, 2582
DSZV, 2583
DT, 2584
DVM, 2585
DZRC, 2586
EDELI, 2587
EDYES, 2588
EEMAP, 2589
EER, 2590
EESR, 2591
EIM, 2592
EIS, 2593
ELIS, 2594
EMDRO, 2595
EMHE, 2596
EMMVP, 2597
EMN, 2598
EMNS, 2599
EMP, 2600
EMRCP, 2601
EMS, 2602
ENLT, 2603
EOMP, 2604
EOPSS, 2605
EPM, 2606
EPSM, 2607
ERMCP, 2608
ESMM, 2609
ETM, 2610
FIMP, 2611
FS, 2612
FTMR, 2613
FVCS, 2614
G, 2615
GEK, 2616
GESD, 2617
GESIS, 2618
GSP, 2619
HMIP, 2620
HMOE, 2621
HMRE, 2622
HMVEI, 2623
HPC, 2624
HPDAA, 2625
HPHI, 2626
HPHID, 2627
HPSMM, 2628
HSC, 2629
ICBM, 2630
ICLT, 2631
IFDVS, 2632
IILT, 2633
ILTB, 2634
ILTD, 2635
ILTIS, 2636
ILTLI, 2637
ILTLT, 2638
IMILT, 2639
IMR, 2640
IP, 2641
IPAC, 2642
IPN, 2643
IPSM, 2644
IPVA, 2645
ISRN, 2646
ITMT, 2647
IVSED, 2648
JCFLT, 2649
KILT, 2650
KLTS, 2651
KNSI, 2652
KPI, 2653
KPIS, 2654
KPLT, 2655
KPNLT, 2656
LIVHS, 2657
LIVRN, 2658
LNSMS, 2659
LSMR, 2660
LTDB, 2661
LTLC, 2662
LTTZZ, 2663
MBLT, 2664
MCT, 2665
ME, 2666
MIMI, 2667
MISM, 2668
MIT, 2669
MIU, 2670
MLTCV, 2671
MLTLT, 2672
MMA, 2673
MMAD, 2674
MMCC, 2675
MMDAA, 2676
MMIM, 2677
MMIP, 2678
MMSMM, 2679
MMT, 2680
MMZM, 2681
MNEM, 2682
MRCB, 2683
MRCLT, 2684
MRMLT, 2685
MRRGE, 2686
MRSLT, 2687
MVSLD, 2688
NEM, 2689
NI, 2690
NJB, 2691
NME1, 2692
NME2, 2693
NME3, 2694
NME4, 2695
NME5, 2696
NME6, 2697
NME7, 2698
NME8, 2699
NME9, 2700
NMLIC, 2701
NMPEM, 2702
NMRRI, 2703
NMTNS, 2704
NMUS, 2705
NOILT, 2706
NPNT, 2707
NSMS, 2708
NVM, 2709
OBNM, 2710
OBUTR, 2711
OD, 2712
OSIS, 2713
OSLI, 2714
PCNA, 2715
PDM, 2716
PEEF, 2717
PIP, 2718
PSMSR, 2719
PSPHS, 2720
PSSD, 2721
PSSLS, 2722
PTMT, 2723
RCLS, 2724
RCSI, 2725
RDS, 2726
REMEF, 2727
REMES, 2728
REMRS, 2729
RGEN, 2730
RLTS, 2731
RMRT, 2732
RNNM, 2733
ROD, 2734
ROSLT, 2735
RPI, 2736
RPNC, 2737
RPNDD, 2738
RREFU, 2739
RSLT, 2740
RSMS, 2741
SCB, 2742
SER, 2743
SLEMM, 2744
SLSLC, 2745
SLTB, 2746
SLTD, 2747
SLTLT, 2748
SMEE, 2749
SMEZV, 2750
SMS, 2751
SMZD, 2752
SMZE, 2753
SNCM, 2754
SS, 2755
SSLD, 2756
SSNS, 2757
SSRLT, 2758
SSS, 2759
SUVB, 2760
SVD, 2761
TD, 2762
TDEE, 2763
technique T, 2764
TIST, 2765
TL, 2766
TMA, 2767
TMSM, 2768
TSE, 2769
TSRM, 2770
TSS, 2771
TT, 2772
TTMI, 2773
UMCOB, 2774
UMI, 2775
UMPIP, 2776
USR, 2777
UTMR, 2778
VFSLS, 2779
VRI, 2780
VRILT, 2781
VRLT, 2782
VRRB, 2783
VRS, 2784
VSLT, 2785
VSPCV, 2786
VSPM, 2787
ZSSM, 2788
ZVSM, 2789
ZVU, 2790
ti83
matrix entry (computation), 2791
row reduce (computation), 2792
vector linear combinations (computation), 2793
TI83 (section), 2794
ti86
matrix entry (computation), 2795
row reduce (computation), 2796
transpose of a matrix (computation), 2797
vector linear combinations (computation), 2798
TI86 (section), 2799
TIS (example), 2800
TIST (theorem), 2801
TIVS (example), 2802
TKAP (example), 2803
TL (theorem), 2804
TLC (example), 2805
TM (definition), 2806
TM (example), 2807
TM (notation), 2808
TM (subsection, section OD), 2809
TM.MMA (computation, section MMA), 2810
TM.SAGE (computation, section SAGE), 2811
TM.TI86 (computation, section TI86), 2812
TMA (theorem), 2813
TMP (example), 2814
TMSM (theorem), 2815
TOV (example), 2816
trace
definition T, 2817
linearity
theorem TL, 2818
matrix multiplication
theorem TSRM, 2819
notation, 2820
similarity
theorem TIST, 2821
sum of eigenvalues
theorem TSE, 2822
trail mix
example TMP, 2823
transpose
matrix scalar multiplication
theorem TMSM, 2824
example TM, 2825
matrix addition
theorem TMA, 2826
matrix inverse, 2827, 2828
notation, 2829
scalar multiplication, 2830
transpose of a matrix
mathematica, 2831
sage, 2832
ti86, 2833
transpose of a transpose
theorem TT, 2834
TREM (example), 2835
triangular decomposition
entry by entry, size 6
example TDEE6, 2836
entry by entry
theorem TDEE, 2837
size 4
example TD4, 2838
solving systems of equations
example TDSSE, 2839
theorem TD, 2840
triangular matrix
inverse
theorem ITMT, 2841
trivial solution
system of equations
definition TSHSE, 2842
TS (definition), 2843
TS (subsection, section S), 2844
TSE (theorem), 2845
TSHSE (definition), 2846
TSM (subsection, section MO), 2847
TSRM (theorem), 2848
TSS (section), 2849
TSS (subsection, section S), 2850
TSS (theorem), 2851
TSVS (definition), 2852
TT (theorem), 2853
TTMI (theorem), 2854
TTS (example), 2855
typical systems, 2 × 2
example TTS, 2856
U (archetype), 2857
U (technique, section PT), 2858
UM (definition), 2859
UM (subsection, section MINM), 2860
UM3 (example), 2861
UMCOB (theorem), 2862
UMI (theorem), 2863
UMPIP (theorem), 2864
unique solution, 3 × 3
example US, 2865
example USR, 2866
uniqueness
technique U, 2867
unit vectors
basis
theorem SUVB, 2868
definition SUV, 2869
orthogonal
example SUVOS, 2870
unitary
permutation matrix
example UPM, 2871
size 3
example UM3, 2872
unitary matrices
columns
theorem CUMOS, 2873
unitary matrix
inner product
theorem UMPIP, 2874
UPM (example), 2875
upper triangular matrix
definition UTM, 2876
US (example), 2877
USR (example), 2878
USR (theorem), 2879
UTM (definition), 2880
UTMR (subsection, section OD), 2881
UTMR (theorem), 2882
V (archetype), 2883
V (chapter), 2884
VA (example), 2885
Vandermonde matrix
definition VM, 2886
vandermonde matrix
determinant
theorem DVM, 2887
nonsingular
theorem NVM, 2888
size 4
example VM4, 2889
VEASM (subsection, section VO), 2890
vector
addition
definition CVA, 2891
column
definition CV, 2892
equality
definition CVE, 2893
notation, 2894
inner product
definition IP, 2895
norm
definition NV, 2896
notation, 2897
of constants
definition VOC, 2898
product with matrix, 2899, 2900
scalar multiplication
definition CVSM, 2901
vector addition
example VA, 2902
vector component
notation, 2903
vector form of solutions
Archetype D
example VFSAD, 2904
Archetype I
example VFSAI, 2905
Archetype L
example VFSAL, 2906
example VFS, 2907
mathematica, 2908
theorem VFSLS, 2909
vector linear combinations
mathematica, 2910
sage, 2911
ti83, 2912
ti86, 2913
vector representation
example AVR, 2914
example VRC4, 2915
injective
theorem VRI, 2916
invertible
theorem VRILT, 2917
linear transformation
definition VR, 2918
notation, 2919
theorem VRLT, 2920
surjective
theorem VRS, 2921
theorem VRRB, 2922
vector representations
polynomials
example VRP2, 2923
vector scalar multiplication
example CVSM, 2924
vector space
characterization
theorem CFDVS, 2925
column vectors
definition VSCV, 2926
definition VS, 2927
infinite dimension
example VSPUD, 2928
linear transformations
theorem VSLT, 2929
over integers mod 5
example VSIM5, 2930
vector space of column vectors
notation, 2931
vector space of functions
example VSF, 2932
vector space of infinite sequences
example VSIS, 2933
vector space of matrices
definition VSM, 2934
example VSM, 2935
notation, 2936
vector space of polynomials
example VSP, 2937
vector space properties
column vectors
theorem VSPCV, 2938
matrices
theorem VSPM, 2939
vector space, crazy
example CVS, 2940
vector space, singleton
example VSS, 2941
vector spaces
isomorphic
definition IVS, 2942
theorem IFDVS, 2943
VESE (example), 2944
VFS (example), 2945
VFSAD (example), 2946
VFSAI (example), 2947
VFSAL (example), 2948
VFSLS (theorem), 2949
VFSS (subsection, section LC), 2950
VFSS.MMA (computation, section MMA), 2951
VLC.MMA (computation, section MMA), 2952
VLC.SAGE (computation, section SAGE), 2953
VLC.TI83 (computation, section TI83), 2954
VLC.TI86 (computation, section TI86), 2955
VM (definition), 2956
VM (section), 2957
VM4 (example), 2958
VO (section), 2959
VOC (definition), 2960
VR (definition), 2961
VR (notation), 2962
VR (section), 2963
VR (subsection, section LISS), 2964
VRC4 (example), 2965
VRI (theorem), 2966
VRILT (theorem), 2967
VRLT (theorem), 2968
VRP2 (example), 2969
VRRB (theorem), 2970
VRS (theorem), 2971
VS (chapter), 2972
VS (definition), 2973
VS (section), 2974
VS (subsection, section VS), 2975
VSCV (definition), 2976
VSCV (example), 2977
VSCV (notation), 2978
VSF (example), 2979
VSIM5 (example), 2980
VSIS (example), 2981
VSLT (theorem), 2982
VSM (definition), 2983
VSM (example), 2984
VSM (notation), 2985
VSP (example), 2986
VSP (subsection, section MO), 2987
VSP (subsection, section VO), 2988
VSP (subsection, section VS), 2989
VSPCV (theorem), 2990
VSPM (theorem), 2991
VSPUD (example), 2992
VSS (example), 2993
W (archetype), 2994
WILA (section), 2995
X (archetype), 2996
Z (Property), 2997
ZC (Property), 2998
ZCN (Property), 2999
ZCV (definition), 3000
ZCV (notation), 3001
zero
complex numbers
Property ZCN, 3002
field
Property ZF, 3003
zero column vector
definition ZCV, 3004
notation, 3005
zero matrix
notation, 3006
zero vector
column vectors
Property ZC, 3007
matrices
Property ZM, 3008
unique
theorem ZVU, 3009
vectors
Property Z, 3010
ZF (Property), 3011
ZM (definition), 3012
ZM (notation), 3013
ZM (Property), 3014
ZNDAB (example), 3015
ZSSM (theorem), 3016
ZVSM (theorem), 3017
ZVU (theorem), 3018