B (archetype), 85
B (definition), 86
B (section), 87
B (subsection, section B), 88
basis
columns nonsingular matrix
example CABAK, 89
common size
theorem BIS, 90
crazy vector apace
example BC, 91
definition B, 92
matrices
example BM, 93
example BSM22, 94
polynomials
example BP, 95
example BPR, 96
example BSP4, 97
example SVP4, 98
subspace of matrices
example BDM22, 99
BC (example), 100
BCS (theorem), 101
BDE (example), 102
BDM22 (example), 103
best cities
money magazine
example MBC, 104
BIS (theorem), 105
BM (example), 106
BNM (subsection, section B), 107
BNS (theorem), 108
BP (example), 109
BPR (example), 110
BRLT (example), 111
BRS (theorem), 112
BS (theorem), 113
BSCV (subsection, section B), 114
BSM22 (example), 115
BSP4 (example), 116
C (archetype), 117
C (definition), 118
C (notation), 119
C (part), 120
C (Property), 121
C (technique, section PT), 122
CABAK (example), 123
CAEHW (example), 124
cancellation
vector addition
theorem VAC, 125
canonical form
nilpotent linear transformation
example CFNLT, 126
theorem CFNLT, 127
CAV (subsection, section O), 128
Cayley-Hamilton
theorem CHT, 129
CB (section), 130
CB (theorem), 131
CBCV (example), 132
CBM (definition), 133
CBM (subsection, section CB), 134
CBP (example), 135
CC (Property), 136
CCCV (definition), 137
CCCV (notation), 138
CCM (definition), 139
CCM (example), 140
CCM (notation), 141
CCN (definition), 142
CCN (notation), 143
CCN (subsection, section CNO), 144
CCRA (theorem), 145
CCRM (theorem), 146
CCT (theorem), 147
CD (subsection, section DM), 148
CD (technique, section PT), 149
CEE (subsection, section EE), 150
CELT (example), 151
CELT (subsection, section CB), 152
CEMS6 (example), 153
CFDVS (theorem), 154
CFNLT (example), 155
CFNLT (subsection, section NLT), 156
CFNLT (theorem), 157
CFV (example), 158
change of basis
between polynomials
example CBP, 159
change-of-basis
between column vectors
example CBCV, 160
matrix representation
theorem MRCB, 161
similarity
theorem SCB, 162
theorem CB, 163
change-of-basis matrix
definition CBM, 164
inverse
theorem ICBM, 165
characteristic polynomial
definition CP, 166
degree
theorem DCP, 167
size 3 matrix
example CPMS3, 168
CHT (subsection, section JCF), 169
CHT (theorem), 170
CILT (subsection, section ILT), 171
CILTI (theorem), 172
CIM (subsection, section MISLE), 173
CINM (theorem), 174
CIVLT (theorem), 175
CLI (theorem), 176
CLTLT (theorem), 177
CM (definition), 178
CM (Property), 179
CM32 (example), 180
CMI (example), 181
CMIAB (example), 182
CMVEI (theorem), 183
CN (appendix), 184
CNA (definition), 185
CNA (notation), 186
CNA (subsection, section CNO), 187
CNE (definition), 188
CNE (notation), 189
CNM (definition), 190
CNM (notation), 191
CNMB (theorem), 192
CNO (section), 193
CNS1 (example), 194
CNS2 (example), 195
CNSV (example), 196
COB (theorem), 197
coefficient matrix
definition CM, 198
nonsingular
theorem SNCM, 199
column space
as null space
theorem FS, 200
Archetype A
example CSAA, 201
Archetype B
example CSAB, 202
as null space
example CSANS, 203
as null space, Archetype G
example FSAG, 204
as row space
theorem CSRST, 205
basis
theorem BCS, 206
consistent system
theorem CSCS, 207
consistent systems
example CSMCS, 208
isomorphic to range, 209
matrix, 210
nonsingular matrix
theorem CSNM, 211
notation, 212
original columns, Archetype D
example CSOCD, 213
row operations, Archetype I
example CSROI, 214
subspace
theorem CSMS, 215
testing membership
example MCSM, 216
two computations
example CSTW, 217
column vector addition
notation, 218
column vector scalar multiplication
notation, 219
commutativity
column vectors
Property CC, 220
matrices
Property CM, 221
vectors
Property C, 222
complex -space
example VSCV, 223
complex arithmetic
example ACN, 224
complex number
conjugate
example CSCN, 225
modulus
example MSCN, 226
complex number
conjugate
definition CCN, 227
modulus
definition MCN, 228
complex numbers
addition
definition CNA, 229
notation, 230
arithmetic properties
theorem PCNA, 231
equality
definition CNE, 232
notation, 233
multiplication
definition CNM, 234
notation, 235
complex vector space
dimension
theorem DCM, 236
composition
injective linear transformations
theorem CILTI, 237
surjective linear transformations
theorem CSLTS, 238
conjugate
addition
theorem CCRA, 239
column vector
definition CCCV, 240
matrix
definition CCM, 241
notation, 242
multiplication
theorem CCRM, 243
notation, 244
scalar multiplication
theorem CRSM, 245
twice
theorem CCT, 246
vector addition
theorem CRVA, 247
conjugate of a vector
notation, 248
conjugation
matrix addition
theorem CRMA, 249
matrix scalar multiplication
theorem CRMSM, 250
matrix transpose
theorem MCT, 251
consistent linear system, 252
consistent linear systems
theorem CSRN, 253
consistent system
definition CS, 254
constructive proofs
technique C, 255
contradiction
technique CD, 256
contrapositive
technique CP, 257
converse
technique CV, 258
coordinates
orthonormal basis
theorem COB, 259
coordinatization
linear combination of matrices
example CM32, 260
linear independence
theorem CLI, 261
orthonormal basis
example CROB3, 262
example CROB4, 263
spanning sets
theorem CSS, 264
coordinatization principle, 265
coordinatizing
polynomials
example CP2, 266
COV (example), 267
COV (subsection, section LDS), 268
CP (definition), 269
CP (subsection, section VR), 270
CP (technique, section PT), 271
CP2 (example), 272
CPMS3 (example), 273
crazy vector space
example CVSR, 274
properties
example PCVS, 275
CRMA (theorem), 276
CRMSM (theorem), 277
CRN (theorem), 278
CROB3 (example), 279
CROB4 (example), 280
CRS (section), 281
CRS (subsection, section FS), 282
CRSM (theorem), 283
CRVA (theorem), 284
CS (definition), 285
CS (example), 286
CS (subsection, section TSS), 287
CSAA (example), 288
CSAB (example), 289
CSANS (example), 290
CSCN (example), 291
CSCS (theorem), 292
CSIP (example), 293
CSLT (subsection, section SLT), 294
CSLTS (theorem), 295
CSM (definition), 296
CSM (notation), 297
CSMCS (example), 298
CSMS (theorem), 299
CSNM (subsection, section CRS), 300
CSNM (theorem), 301
CSOCD (example), 302
CSRN (theorem), 303
CSROI (example), 304
CSRST (theorem), 305
CSS (theorem), 306
CSSE (subsection, section CRS), 307
CSSM (theorem), 308
CSSOC (subsection, section CRS), 309
CSTW (example), 310
CTLT (example), 311
CUMOS (theorem), 312
CV (definition), 313
CV (notation), 314
CV (technique, section PT), 315
CVA (definition), 316
CVA (notation), 317
CVC (notation), 318
CVE (definition), 319
CVE (notation), 320
CVS (example), 321
CVS (subsection, section VR), 322
CVSM (definition), 323
CVSM (example), 324
CVSM (notation), 325
CVSM (theorem), 326
CVSR (example), 327
D (archetype), 328
D (chapter), 329
D (definition), 330
D (notation), 331
D (section), 332
D (subsection, section D), 333
D (subsection, section SD), 334
D (technique, section PT), 335
D33M (example), 336
DAB (example), 337
DC (example), 338
DC (technique, section PT), 339
DC (theorem), 340
DCM (theorem), 341
DCN (Property), 342
DCP (theorem), 343
DD (subsection, section DM), 344
DEC (theorem), 345
decomposition
technique DC, 346
DED (theorem), 347
definition
A, 348
AM, 349
AME, 350
B, 351
C, 352
CBM, 353
CCCV, 354
CCM, 355
CCN, 356
CM, 357
CNA, 358
CNE, 359
CNM, 360
CP, 361
CS, 362
CSM, 363
CV, 364
CVA, 365
CVE, 366
CVSM, 367
D, 368
DIM, 369
DM, 370
DS, 371
DZM, 372
EEF, 373
EELT, 374
EEM, 375
ELEM, 376
EM, 377
EO, 378
ES, 379
ESYS, 380
F, 381
GES, 382
GEV, 383
GME, 384
HM, 385
HS, 386
IDLT, 387
IDV, 388
IE, 389
ILT, 390
IM, 391
IMP, 392
IP, 393
IS, 394
IVLT, 395
IVS, 396
JB, 397
JCF, 398
KLT, 399
LC, 400
LCCV, 401
LI, 402
LICV, 403
LNS, 404
LSMR, 405
LT, 406
LTA, 407
LTC, 408
LTR, 409
LTSM, 410
M, 411
MA, 412
MCN, 413
ME, 414
MI, 415
MM, 416
MR, 417
MSM, 418
MVP, 419
NLT, 420
NM, 421
NOLT, 422
NOM, 423
NSM, 424
NV, 425
ONS, 426
OSV, 427
OV, 428
PI, 429
REM, 430
RLD, 431
RLDCV, 432
RLT, 433
RO, 434
ROLT, 435
ROM, 436
RR, 437
RREF, 438
RSM, 439
S, 440
SC, 441
SE, 442
SET, 443
SI, 444
SIM, 445
SLE, 446
SLT, 447
SM, 448
SQM, 449
SS, 450
SSCV, 451
SSET, 452
SU, 453
SUV, 454
SV, 455
SYM, 456
technique D, 457
TM, 458
TS, 459
TSHSE, 460
TSVS, 461
UM, 462
VOC, 463
VR, 464
VS, 465
VSCV, 466
VSM, 467
ZCV, 468
ZM, 469
DEHD (example), 470
DEM (theorem), 471
DEMMM (theorem), 472
DEMS5 (example), 473
DER (theorem), 474
DERC (theorem), 475
determinant
computed two ways
example TCSD, 476
definition DM, 477
equal rows or columns
theorem DERC, 478
expansion, columns
theorem DEC, 479
expansion, rows
theorem DER, 480
identity matrix
theorem DIM, 481
matrix multiplication
theorem DRMM, 482
nonsingular matrix, 483
notation, 484
row or column multiple
theorem DRCM, 485
row or column swap
theorem DRCS, 486
size 2 matrix
theorem DMST, 487
size 3 matrix
example D33M, 488
transpose
theorem DT, 489
via row operations
example DRO, 490
zero
theorem SMZD, 491
zero row or column
theorem DZRC, 492
zero versus nonzero
example ZNDAB, 493
determinant, upper triangular matrix
example DUTM, 494
determinants
elementary matrices
theorem DEMMM, 495
DF (Property), 496
DFS (subsection, section PD), 497
DFS (theorem), 498
DGES (theorem), 499
diagonal matrix
definition DIM, 500
diagonalizable
definition DZM, 501
distinct eigenvalues
example DEHD, 502
theorem DED, 503
full eigenspaces
theorem DMFE, 504
not
example NDMS4, 505
diagonalizable matrix
high power
example HPDM, 506
diagonalization
Archetype B
example DAB, 507
criteria
theorem DC, 508
example DMS3, 509
DIM (definition), 510
DIM (theorem), 511
dimension
crazy vector space
example DC, 512
definition D, 513
notation, 514
polynomial subspace
example DSP4, 515
proper subspaces
theorem PSSD, 516
subspace
example DSM22, 517
direct sum
decomposing zero vector
theorem DSZV, 518
definition DS, 519
dimension
theorem DSD, 520
example SDS, 521
from a basis
theorem DSFB, 522
from one subspace
theorem DSFOS, 523
notation, 524
zero intersection
theorem DSZI, 525
direct sums
linear independence
theorem DSLI, 526
repeated
theorem RDS, 527
distributivity
complex numbers
Property DCN, 528
field
Property DF, 529
distributivity, matrix addition
matrices
Property DMAM, 530
distributivity, scalar addition
column vectors
Property DSAC, 531
matrices
Property DSAM, 532
vectors
Property DSA, 533
distributivity, vector addition
column vectors
Property DVAC, 534
vectors
Property DVA, 535
DLDS (theorem), 536
DM (definition), 537
DM (notation), 538
DM (section), 539
DM (theorem), 540
DMAM (Property), 541
DMFE (theorem), 542
DMS3 (example), 543
DMST (theorem), 544
DNLT (theorem), 545
DNMMM (subsection, section PDM), 546
DP (theorem), 547
DRCM (theorem), 548
DRCMA (theorem), 549
DRCS (theorem), 550
DRMM (theorem), 551
DRO (example), 552
DRO (subsection, section PDM), 553
DROEM (subsection, section PDM), 554
DS (definition), 555
DS (notation), 556
DS (subsection, section PD), 557
DSA (Property), 558
DSAC (Property), 559
DSAM (Property), 560
DSD (theorem), 561
DSFB (theorem), 562
DSFOS (theorem), 563
DSLI (theorem), 564
DSM22 (example), 565
DSP4 (example), 566
DSZI (theorem), 567
DSZV (theorem), 568
DT (theorem), 569
DUTM (example), 570
DVA (Property), 571
DVAC (Property), 572
DVS (subsection, section D), 573
DZM (definition), 574
DZRC (theorem), 575
E (archetype), 576
E (chapter), 577
E (technique, section PT), 578
ECEE (subsection, section EE), 579
EDELI (theorem), 580
EDYES (theorem), 581
EE (section), 582
EEE (subsection, section EE), 583
EEF (definition), 584
EEF (subsection, section FS), 585
EELT (definition), 586
EELT (subsection, section CB), 587
EEM (definition), 588
EEM (subsection, section EE), 589
EENS (example), 590
EER (theorem), 591
EHM (subsection, section PEE), 592
eigenspace
as null space
theorem EMNS, 593
definition EM, 594
invariant subspace
theorem EIS, 595
subspace
theorem EMS, 596
eigenvalue
algebraic multiplicity
definition AME, 597
complex
example CEMS6, 598
definition EEM, 599
existence
example CAEHW, 600
theorem EMHE, 601
geometric multiplicity
definition GME, 602
index, 603
linear transformation
definition EELT, 604
multiplicities
example EMMS4, 605
power
theorem EOMP, 606
root of characteristic polynomial
theorem EMRCP, 607
scalar multiple
theorem ESMM, 608
symmetric matrix
example ESMS4, 609
zero
theorem SMZE, 610
eigenvalues
building desired
example BDE, 611
complex, of a linear transformation
example CELT, 612
conjugate pairs
theorem ERMCP, 613
distinct
example DEMS5, 614
example SEE, 615
Hermitian matrices
theorem HMRE, 616
inverse
theorem EIM, 617
maximum number
theorem MNEM, 618
multiplicities
example HMEM5, 619
theorem ME, 620
number
theorem NEM, 621
of a polynomial
theorem EPM, 622
size 3 matrix
example EMS3, 623
example ESMS3, 624
transpose
theorem ETM, 625
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 626
eigenvector, 627
linear transformation, 628
eigenvectors, 629
conjugate pairs, 630
Hermitian matrices
theorem HMOE, 631
linear transformation
example ELTBM, 632
example ELTBP, 633
linearly independent
theorem EDELI, 634
of a linear transformation
example ELTT, 635
EILT (subsection, section ILT), 636
EIM (theorem), 637
EIS (example), 638
EIS (theorem), 639
ELEM (definition), 640
ELEM (notation), 641
elementary matrices
definition ELEM, 642
determinants
theorem DEM, 643
nonsingular
theorem EMN, 644
notation, 645
row operations
example EMRO, 646
theorem EMDRO, 647
ELIS (theorem), 648
ELTBM (example), 649
ELTBP (example), 650
ELTT (example), 651
EM (definition), 652
EM (subsection, section DM), 653
EMDRO (theorem), 654
EMHE (theorem), 655
EMMS4 (example), 656
EMMVP (theorem), 657
EMN (theorem), 658
EMNS (theorem), 659
EMP (theorem), 660
empty set, 661
notation, 662
EMRCP (theorem), 663
EMRO (example), 664
EMS (theorem), 665
EMS3 (example), 666
ENLT (theorem), 667
EO (definition), 668
EOMP (theorem), 669
EOPSS (theorem), 670
EPM (theorem), 671
equal matrices
via equal matrix-vector products
theorem EMMVP, 672
equation operations
definition EO, 673
theorem EOPSS, 674
equivalence statements
technique E, 675
equivalences
technique ME, 676
equivalent systems
definition ESYS, 677
ERMCP (theorem), 678
ES (definition), 679
ES (notation), 680
ESEO (subsection, section SSLE), 681
ESLT (subsection, section SLT), 682
ESMM (theorem), 683
ESMS3 (example), 684
ESMS4 (example), 685
ESYS (definition), 686
ETM (theorem), 687
EVS (subsection, section VS), 688
example
AALC, 689
ABLC, 690
ABS, 691
ACN, 692
AHSAC, 693
AIVLT, 694
ALT, 695
ALTMM, 696
AM, 697
AMAA, 698
ANILT, 699
AOS, 700
ASC, 701
AVR, 702
BC, 703
BDE, 704
BDM22, 705
BM, 706
BP, 707
BPR, 708
BRLT, 709
BSM22, 710
BSP4, 711
CABAK, 712
CAEHW, 713
CBCV, 714
CBP, 715
CCM, 716
CELT, 717
CEMS6, 718
CFNLT, 719
CFV, 720
CM32, 721
CMI, 722
CMIAB, 723
CNS1, 724
CNS2, 725
CNSV, 726
COV, 727
CP2, 728
CPMS3, 729
CROB3, 730
CROB4, 731
CS, 732
CSAA, 733
CSAB, 734
CSANS, 735
CSCN, 736
CSIP, 737
CSMCS, 738
CSOCD, 739
CSROI, 740
CSTW, 741
CTLT, 742
CVS, 743
CVSM, 744
CVSR, 745
D33M, 746
DAB, 747
DC, 748
DEHD, 749
DEMS5, 750
DMS3, 751
DRO, 752
DSM22, 753
DSP4, 754
DUTM, 755
EENS, 756
EIS, 757
ELTBM, 758
ELTBP, 759
ELTT, 760
EMMS4, 761
EMRO, 762
EMS3, 763
ESMS3, 764
ESMS4, 765
FDV, 766
FF8, 767
FRAN, 768
FS1, 769
FS2, 770
FSAG, 771
GE4, 772
GE6, 773
GENR6, 774
GSTV, 775
HISAA, 776
HISAD, 777
HMEM5, 778
HPDM, 779
HUSAB, 780
IAP, 781
IAR, 782
IAS, 783
IAV, 784
ILTVR, 785
IM, 786
IM11, 787
IS, 788
ISJB, 789
ISMR4, 790
ISMR6, 791
ISSI, 792
IVSAV, 793
JB4, 794
JCF10, 795
KPNLT, 796
KVMR, 797
LCM, 798
LDCAA, 799
LDHS, 800
LDP4, 801
LDRN, 802
LDS, 803
LIC, 804
LICAB, 805
LIHS, 806
LIM32, 807
LINSB, 808
LIP4, 809
LIS, 810
LLDS, 811
LNS, 812
LTDB1, 813
LTDB2, 814
LTDB3, 815
LTM, 816
LTPM, 817
LTPP, 818
MA, 819
MBC, 820
MCSM, 821
MFLT, 822
MI, 823
MIVS, 824
MMNC, 825
MNSLE, 826
MOLT, 827
MPMR, 828
MRBE, 829
MRCM, 830
MSCN, 831
MSM, 832
MTV, 833
MWIAA, 834
NDMS4, 835
NIAO, 836
NIAQ, 837
NIAQR, 838
NIDAU, 839
NJB5, 840
NKAO, 841
NLT, 842
NM, 843
NM62, 844
NM64, 845
NM83, 846
NRREF, 847
NSAO, 848
NSAQ, 849
NSAQR, 850
NSC2A, 851
NSC2S, 852
NSC2Z, 853
NSDAT, 854
NSDS, 855
NSE, 856
NSEAI, 857
NSLE, 858
NSLIL, 859
NSNM, 860
NSR, 861
NSS, 862
OLTTR, 863
ONFV, 864
ONTV, 865
OSGMD, 866
OSMC, 867
PCVS, 868
PM, 869
PSHS, 870
PTM, 871
PTMEE, 872
RAO, 873
RES, 874
RNM, 875
RNSM, 876
ROD2, 877
ROD4, 878
RREF, 879
RREFN, 880
RRTI, 881
RS, 882
RSAI, 883
RSB, 884
RSC5, 885
RSNS, 886
RSREM, 887
RSSC4, 888
RVMR, 889
S, 890
SAA, 891
SAB, 892
SABMI, 893
SAE, 894
SAN, 895
SAR, 896
SAV, 897
SC, 898
SC3, 899
SCAA, 900
SCAB, 901
SCAD, 902
SDS, 903
SEE, 904
SEEF, 905
SETM, 906
SI, 907
SM2Z7, 908
SM32, 909
SMLT, 910
SMS3, 911
SMS5, 912
SP4, 913
SPIAS, 914
SRR, 915
SS, 916
SSC, 917
SSET, 918
SSM22, 919
SSNS, 920
SSP, 921
SSP4, 922
STLT, 923
STNE, 924
SU, 925
SUVOS, 926
SVP4, 927
SYM, 928
TCSD, 929
TIS, 930
TIVS, 931
TKAP, 932
TLC, 933
TM, 934
TMP, 935
TOV, 936
TREM, 937
TTS, 938
UM3, 939
UPM, 940
US, 941
USR, 942
VA, 943
VESE, 944
VFS, 945
VFSAD, 946
VFSAI, 947
VFSAL, 948
VRC4, 949
VRP2, 950
VSCV, 951
VSF, 952
VSIM5, 953
VSIS, 954
VSM, 955
VSP, 956
VSPUD, 957
VSS, 958
ZNDAB, 959
EXC (subsection, section B), 960
EXC (subsection, section CB), 961
EXC (subsection, section CRS), 962
EXC (subsection, section D), 963
EXC (subsection, section DM), 964
EXC (subsection, section EE), 965
EXC (subsection, section F), 966
EXC (subsection, section FS), 967
EXC (subsection, section HSE), 968
EXC (subsection, section ILT), 969
EXC (subsection, section IVLT), 970
EXC (subsection, section LC), 971
EXC (subsection, section LDS), 972
EXC (subsection, section LI), 973
EXC (subsection, section LISS), 974
EXC (subsection, section LT), 975
EXC (subsection, section MINM), 976
EXC (subsection, section MISLE), 977
EXC (subsection, section MM), 978
EXC (subsection, section MO), 979
EXC (subsection, section MR), 980
EXC (subsection, section NM), 981
EXC (subsection, section O), 982
EXC (subsection, section PD), 983
EXC (subsection, section PDM), 984
EXC (subsection, section PEE), 985
EXC (subsection, section RREF), 986
EXC (subsection, section S), 987
EXC (subsection, section SD), 988
EXC (subsection, section SLT), 989
EXC (subsection, section SS), 990
EXC (subsection, section SSLE), 991
EXC (subsection, section TSS), 992
EXC (subsection, section VO), 993
EXC (subsection, section VR), 994
EXC (subsection, section VS), 995
EXC (subsection, section WILA), 996
extended echelon form
submatrices
example SEEF, 997
extended reduced row-echelon form
properties
theorem PEEF, 998
F (archetype), 999
F (definition), 1000
F (section), 1001
F (subsection, section F), 1002
FDV (example), 1003
FF (subsection, section F), 1004
FF8 (example), 1005
field
definition F, 1006
FIMP (theorem), 1007
finite field
size 8
example FF8, 1008
four subsets
example FS1, 1009
example FS2, 1010
four subspaces
dimension
theorem DFS, 1011
FRAN (example), 1012
free variables
example CFV, 1013
free variables, number
theorem FVCS, 1014
free, independent variables
example FDV, 1015
FS (section), 1016
FS (subsection, section FS), 1017
FS (theorem), 1018
FS1 (example), 1019
FS2 (example), 1020
FSAG (example), 1021
FTMR (theorem), 1022
FV (subsection, section TSS), 1023
FVCS (theorem), 1024
G (archetype), 1025
G (theorem), 1026
GE4 (example), 1027
GE6 (example), 1028
GEE (subsection, section IS), 1029
GEK (theorem), 1030
generalized eigenspace
as kernel
theorem GEK, 1031
definition GES, 1032
dimension
theorem DGES, 1033
dimension 4 domain
example GE4, 1034
dimension 6 domain
example GE6, 1035
invariant subspace
theorem GESIS, 1036
nilpotent restriction
theorem RGEN, 1037
nilpotent restrictions, dimension 6 domain
example GENR6, 1038
notation, 1039
generalized eigenspace decomposition
theorem GESD, 1040
generalized eigenvector
definition GEV, 1041
GENR6 (example), 1042
GES (definition), 1043
GES (notation), 1044
GESD (subsection, section JCF), 1045
GESD (theorem), 1046
GESIS (theorem), 1047
GEV (definition), 1048
GFDL (appendix), 1049
GME (definition), 1050
goldilocks
theorem G, 1051
Gram-Schmidt
column vectors
theorem GSPCV, 1052
three vectors
example GSTV, 1053
gram-schmidt
mathematica, 1054
GS (technique, section PT), 1055
GSP (subsection, section O), 1056
GSP.MMA (computation, section MMA), 1057
GSPCV (theorem), 1058
GSTV (example), 1059
GT (subsection, section PD), 1060
H (archetype), 1061
hermitian
definition HM, 1062
HISAA (example), 1063
HISAD (example), 1064
HM (definition), 1065
HMEM5 (example), 1066
HMOE (theorem), 1067
HMRE (theorem), 1068
HMVEI (theorem), 1069
homogeneous system
consistent
theorem HSC, 1070
definition HS, 1071
infinitely many solutions
theorem HMVEI, 1072
homogeneous systems
linear independence, 1073
homogenous system
Archetype C
example AHSAC, 1074
HPDM (example), 1075
HS (definition), 1076
HSC (theorem), 1077
HSE (section), 1078
HUSAB (example), 1079
I (archetype), 1080
I (technique, section PT), 1081
IAP (example), 1082
IAR (example), 1083
IAS (example), 1084
IAV (example), 1085
ICBM (theorem), 1086
ICLT (theorem), 1087
identities
technique PI, 1088
identity matrix
determinant, 1089
example IM, 1090
notation, 1091
IDLT (definition), 1092
IDV (definition), 1093
IE (definition), 1094
IE (notation), 1095
IFDVS (theorem), 1096
IILT (theorem), 1097
ILT (definition), 1098
ILT (section), 1099
ILTB (theorem), 1100
ILTD (subsection, section ILT), 1101
ILTD (theorem), 1102
ILTIS (theorem), 1103
ILTLI (subsection, section ILT), 1104
ILTLI (theorem), 1105
ILTLT (theorem), 1106
ILTVR (example), 1107
IM (definition), 1108
IM (example), 1109
IM (notation), 1110
IM (subsection, section MISLE), 1111
IM11 (example), 1112
IMILT (theorem), 1113
IMP (definition), 1114
IMR (theorem), 1115
inconsistent linear systems
theorem ISRN, 1116
independent, dependent variables
definition IDV, 1117
indesxstring
example SM2Z7, 1118
example SSET, 1119
index
eigenvalue
definition IE, 1120
notation, 1121
indexstring
theorem DRCMA, 1122
induction
technique I, 1123
infinite solution set
example ISSI, 1124
infinite solutions,
example IS, 1125
injective
example IAP, 1126
example IAR, 1127
not
example NIAO, 1128
example NIAQ, 1129
example NIAQR, 1130
not, by dimension
example NIDAU, 1131
polynomials to matrices
example IAV, 1132
injective linear transformation
bases
theorem ILTB, 1133
injective linear transformations
dimension
theorem ILTD, 1134
inner product
anti-commutative
theorem IPAC, 1135
example CSIP, 1136
norm
theorem IPN, 1137
notation, 1138
positive
theorem PIP, 1139
scalar multiplication
theorem IPSM, 1140
vector addition
theorem IPVA, 1141
integers
mod
definition IMP, 1142
mod ,
field
theorem FIMP, 1143
mod 11
example IM11, 1144
invariant subspace
definition IS, 1145
eigenspace, 1146
eigenspaces
example EIS, 1147
example TIS, 1148
Jordan block
example ISJB, 1149
kernels of powers
theorem KPIS, 1150
inverse
composition of linear transformations
theorem ICLT, 1151
example CMI, 1152
example MI, 1153
notation, 1154
of a matrix, 1155
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1156
invertible linear transformations
composition
theorem CIVLT, 1157
IP (definition), 1158
IP (notation), 1159
IP (subsection, section O), 1160
IPAC (theorem), 1161
IPN (theorem), 1162
IPSM (theorem), 1163
IPVA (theorem), 1164
IS (definition), 1165
IS (example), 1166
IS (section), 1167
IS (subsection, section IS), 1168
ISJB (example), 1169
ISMR4 (example), 1170
ISMR6 (example), 1171
isomorphic
multiple vector spaces
example MIVS, 1172
vector spaces
example IVSAV, 1173
isomorphic vector spaces
dimension
theorem IVSED, 1174
example TIVS, 1175
ISRN (theorem), 1176
ISSI (example), 1177
IV (subsection, section IVLT), 1178
IVLT (definition), 1179
IVLT (section), 1180
IVLT (subsection, section IVLT), 1181
IVLT (subsection, section MR), 1182
IVS (definition), 1183
IVSAV (example), 1184
IVSED (theorem), 1185
J (archetype), 1186
JB (definition), 1187
JB (notation), 1188
JB4 (example), 1189
JCF (definition), 1190
JCF (section), 1191
JCF (subsection, section JCF), 1192
JCF10 (example), 1193
JCFLT (theorem), 1194
Jordan block
definition JB, 1195
nilpotent
theorem NJB, 1196
notation, 1197
size 4
example JB4, 1198
Jordan canonical form
definition JCF, 1199
size 10
example JCF10, 1200
K (archetype), 1201
kernel
injective linear transformation
theorem KILT, 1202
isomorphic to null space
theorem KNSI, 1203
linear transformation
example NKAO, 1204
notation, 1205
of a linear transformation
definition KLT, 1206
pre-image, 1207
subspace
theorem KLTS, 1208
trivial
example TKAP, 1209
via matrix representation
example KVMR, 1210
KILT (theorem), 1211
KLT (definition), 1212
KLT (notation), 1213
KLT (subsection, section ILT), 1214
KLTS (theorem), 1215
KNSI (theorem), 1216
KPI (theorem), 1217
KPIS (theorem), 1218
KPLT (theorem), 1219
KPNLT (example), 1220
KPNLT (theorem), 1221
KVMR (example), 1222
L (archetype), 1223
L (technique, section PT), 1224
LA (subsection, section WILA), 1225
LC (definition), 1226
LC (section), 1227
LC (subsection, section LC), 1228
LC (technique, section PT), 1229
LCCV (definition), 1230
LCM (example), 1231
LDCAA (example), 1232
LDHS (example), 1233
LDP4 (example), 1234
LDRN (example), 1235
LDS (example), 1236
LDS (section), 1237
LDSS (subsection, section LDS), 1238
left null space
as row space, 1239
definition LNS, 1240
example LNS, 1241
notation, 1242
subspace
theorem LNSMS, 1243
lemma
technique LC, 1244
LI (definition), 1245
LI (section), 1246
LI (subsection, section LISS), 1247
LIC (example), 1248
LICAB (example), 1249
LICV (definition), 1250
LIHS (example), 1251
LIM32 (example), 1252
linear combination
system of equations
example ABLC, 1253
definition LC, 1254
definition LCCV, 1255
example TLC, 1256
linear transformation, 1257
matrices
example LCM, 1258
system of equations
example AALC, 1259
linear combinations
solutions to linear systems
theorem SLSLC, 1260
linear dependence
more vectors than size
theorem MVSLD, 1261
linear independence
definition LI, 1262
definition LICV, 1263
homogeneous systems
theorem LIVHS, 1264
injective linear transformation
theorem ILTLI, 1265
matrices
example LIM32, 1266
orthogonal, 1267
r and n
theorem LIVRN, 1268
linear solve
mathematica, 1269
linear system
consistent
theorem RCLS, 1270
matrix representation
definition LSMR, 1271
notation, 1272
linear systems
notation
example MNSLE, 1273
example NSLE, 1274
linear transformation
polynomials to polynomials
example LTPP, 1275
addition
definition LTA, 1276
theorem MLTLT, 1277
theorem SLTLT, 1278
as matrix multiplication
example ALTMM, 1279
basis of range
example BRLT, 1280
checking
example ALT, 1281
composition
definition LTC, 1282
theorem CLTLT, 1283
defined by a matrix
example LTM, 1284
defined on a basis
example LTDB1, 1285
example LTDB2, 1286
example LTDB3, 1287
theorem LTDB, 1288
definition LT, 1289
identity
definition IDLT, 1290
injection
definition ILT, 1291
inverse
theorem ILTLT, 1292
inverse of inverse
theorem IILT, 1293
invertible
definition IVLT, 1294
example AIVLT, 1295
invertible, injective and surjective
theorem ILTIS, 1296
Jordan canonical form
theorem JCFLT, 1297
kernels of powers
theorem KPLT, 1298
linear combination
theorem LTLC, 1299
matrix of, 1300
example MFLT, 1301
example MOLT, 1302
not
example NLT, 1303
not invertible
example ANILT, 1304
notation, 1305
polynomials to matrices
example LTPM, 1306
rank plus nullity
theorem RPNDD, 1307
restriction
definition LTR, 1308
notation, 1309
scalar multiple
example SMLT, 1310
scalar multiplication
definition LTSM, 1311
spanning range
theorem SSRLT, 1312
sum
example STLT, 1313
surjection
definition SLT, 1314
vector space of, 1315
zero vector
theorem LTTZZ, 1316
linear transformation inverse
via matrix representation
example ILTVR, 1317
linear transformations
compositions
example CTLT, 1318
from matrices
theorem MBLT, 1319
linearly dependent
example LDRN, 1320
via homogeneous system
example LDHS, 1321
linearly dependent columns
Archetype A
example LDCAA, 1322
linearly dependent set
example LDS, 1323
linear combinations within
theorem DLDS, 1324
polynomials
example LDP4, 1325
linearly independent
crazy vector space
example LIC, 1326
extending sets
theorem ELIS, 1327
polynomials
example LIP4, 1328
via homogeneous system
example LIHS, 1329
linearly independent columns
Archetype B
example LICAB, 1330
linearly independent set
example LIS, 1331
example LLDS, 1332
LINM (subsection, section LI), 1333
LINSB (example), 1334
LIP4 (example), 1335
LIS (example), 1336
LISS (section), 1337
LISV (subsection, section LI), 1338
LIVHS (theorem), 1339
LIVRN (theorem), 1340
LLDS (example), 1341
LNS (definition), 1342
LNS (example), 1343
LNS (notation), 1344
LNS (subsection, section FS), 1345
LNSMS (theorem), 1346
LS.MMA (computation, section MMA), 1347
LSMR (definition), 1348
LSMR (notation), 1349
LT (chapter), 1350
LT (definition), 1351
LT (notation), 1352
LT (section), 1353
LT (subsection, section LT), 1354
LTA (definition), 1355
LTC (definition), 1356
LTDB (theorem), 1357
LTDB1 (example), 1358
LTDB2 (example), 1359
LTDB3 (example), 1360
LTLC (subsection, section LT), 1361
LTLC (theorem), 1362
LTM (example), 1363
LTPM (example), 1364
LTPP (example), 1365
LTR (definition), 1366
LTR (notation), 1367
LTSM (definition), 1368
LTTZZ (theorem), 1369
M (archetype), 1370
M (chapter), 1371
M (definition), 1372
M (notation), 1373
MA (definition), 1374
MA (example), 1375
MA (notation), 1376
MACN (Property), 1377
MAF (Property), 1378
mathematica
gram-schmidt (computation), 1379
linear solve (computation), 1380
matrix entry (computation), 1381
matrix inverse (computation), 1382
matrix multiplication (computation), 1383
null space (computation), 1384
row reduce (computation), 1385
transpose of a matrix (computation), 1386
vector form of solutions (computation), 1387
vector linear combinations (computation), 1388
mathematical language
technique L, 1389
matrix
addition
definition MA, 1390
notation, 1391
augmented
definition AM, 1392
column space
definition CSM, 1393
complex conjugate
example CCM, 1394
definition M, 1395
equality
definition ME, 1396
notation, 1397
example AM, 1398
identity
definition IM, 1399
inverse
definition MI, 1400
nonsingular
definition NM, 1401
notation, 1402
of a linear transformation
theorem MLTCV, 1403
product
example PTM, 1404
example PTMEE, 1405
product with vector
definition MVP, 1406
rectangular, 1407
row space
definition RSM, 1408
scalar multiplication
definition MSM, 1409
notation, 1410
singular, 1411
square
definition SQM, 1412
submatrices
example SS, 1413
submatrix
definition SM, 1414
symmetric
definition SYM, 1415
transpose
definition TM, 1416
unitary
definition UM, 1417
unitary is invertible
theorem UMI, 1418
zero
definition ZM, 1419
matrix addition
example MA, 1420
matrix components
notation, 1421
matrix entry
mathematica, 1422
ti83, 1423
ti86, 1424
matrix inverse
Archetype B, 1425
computation
theorem CINM, 1426
mathematica, 1427
nonsingular matrix
theorem NI, 1428
of a matrix inverse
theorem MIMI, 1429
one-sided
theorem OSIS, 1430
product
theorem SS, 1431
scalar multiple
theorem MISM, 1432
size 2 matrices
theorem TTMI, 1433
transpose
theorem MIT, 1434
uniqueness
theorem MIU, 1435
matrix multiplication
associativity
theorem MMA, 1436
complex conjugation
theorem MMCC, 1437
definition MM, 1438
distributivity
theorem MMDAA, 1439
entry-by-entry
theorem EMP, 1440
identity matrix
theorem MMIM, 1441
inner product
theorem MMIP, 1442
mathematica, 1443
noncommutative
example MMNC, 1444
scalar matrix multiplication
theorem MMSMM, 1445
systems of linear equations
theorem SLEMM, 1446
transposes
theorem MMT, 1447
zero matrix
theorem MMZM, 1448
matrix product
as composition of linear transformations
example MPMR, 1449
matrix representation
basis of eigenvectors
example MRBE, 1450
composition of linear transformations
theorem MRCLT, 1451
definition MR, 1452
invertible
theorem IMR, 1453
multiple of a linear transformation
theorem MRMLT, 1454
restriction to generalized eigenspace
theorem MRRGE, 1455
sum of linear transformations
theorem MRSLT, 1456
theorem FTMR, 1457
upper-triangular
theorem UTMR, 1458
matrix representations
converting with change-of-basis
example MRCM, 1459
example OLTTR, 1460
matrix scalar multiplication
example MSM, 1461
matrix vector space
dimension
theorem DM, 1462
matrix-vector product
example MTV, 1463
notation, 1464
MBC (example), 1465
MBLT (theorem), 1466
MC (notation), 1467
MCC (subsection, section MO), 1468
MCCN (Property), 1469
MCF (Property), 1470, 1471
MCN (definition), 1472
MCN (subsection, section CNO), 1473
MCSM (example), 1474
MCT (theorem), 1475
MD (chapter), 1476
ME (definition), 1477
ME (notation), 1478
ME (subsection, section PEE), 1479
ME (technique, section PT), 1480
ME (theorem), 1481
ME.MMA (computation, section MMA), 1482
ME.TI83 (computation, section TI83), 1483
ME.TI86 (computation, section TI86), 1484
MEASM (subsection, section MO), 1485
MFLT (example), 1486
MI (definition), 1487
MI (example), 1488
MI (notation), 1489
MI.MMA (computation, section MMA), 1490
MICN (Property), 1491
MIF (Property), 1492
MIMI (theorem), 1493
MINM (section), 1494
MISLE (section), 1495
MISM (theorem), 1496
MIT (theorem), 1497
MIU (theorem), 1498
MIVS (example), 1499
MLT (subsection, section LT), 1500
MLTCV (theorem), 1501
MLTLT (theorem), 1502
MM (definition), 1503
MM (section), 1504
MM (subsection, section MM), 1505
MM.MMA (computation, section MMA), 1506
MMA (section), 1507
MMA (theorem), 1508
MMCC (theorem), 1509
MMDAA (theorem), 1510
MMEE (subsection, section MM), 1511
MMIM (theorem), 1512
MMIP (theorem), 1513
MMNC (example), 1514
MMSMM (theorem), 1515
MMT (theorem), 1516
MMZM (theorem), 1517
MNEM (theorem), 1518
MNSLE (example), 1519
MO (section), 1520
MOLT (example), 1521
more variables than equations
example OSGMD, 1522
theorem CMVEI, 1523
MPMR (example), 1524
MR (definition), 1525
MR (section), 1526
MRBE (example), 1527
MRCB (theorem), 1528
MRCLT (theorem), 1529
MRCM (example), 1530
MRMLT (theorem), 1531
MRRGE (theorem), 1532
MRS (subsection, section CB), 1533
MRSLT (theorem), 1534
MSCN (example), 1535
MSM (definition), 1536
MSM (example), 1537
MSM (notation), 1538
MTV (example), 1539
multiplicative associativity
complex numbers
Property MACN, 1540
multiplicative closure
field
Property MCF, 1541
multiplicative commuativity
complex numbers
Property MCCN, 1542
multiplicative inverse
complex numbers
Property MICN, 1543
MVNSE (subsection, section RREF), 1544
MVP (definition), 1545
MVP (notation), 1546
MVP (subsection, section MM), 1547
MVSLD (theorem), 1548
MWIAA (example), 1549
N (archetype), 1550
N (subsection, section O), 1551
N (technique, section PT), 1552
NDMS4 (example), 1553
negation of statements
technique N, 1554
NEM (theorem), 1555
NI (theorem), 1556
NIAO (example), 1557
NIAQ (example), 1558
NIAQR (example), 1559
NIDAU (example), 1560
nilpotent
linear transformation
definition NLT, 1561
NJB (theorem), 1562
NJB5 (example), 1563
NKAO (example), 1564
NLT (definition), 1565
NLT (example), 1566
NLT (section), 1567
NLT (subsection, section NLT), 1568
NLTFO (subsection, section LT), 1569
NM (definition), 1570
NM (example), 1571
NM (section), 1572
NM (subsection, section NM), 1573
NM62 (example), 1574
NM64 (example), 1575
NM83 (example), 1576
NME1 (theorem), 1577
NME2 (theorem), 1578
NME3 (theorem), 1579
NME4 (theorem), 1580
NME5 (theorem), 1581
NME6 (theorem), 1582
NME7 (theorem), 1583
NME8 (theorem), 1584
NME9 (theorem), 1585
NMI (subsection, section MINM), 1586
NMLIC (theorem), 1587
NMPEM (theorem), 1588
NMRRI (theorem), 1589
NMTNS (theorem), 1590
NMUS (theorem), 1591
NOILT (theorem), 1592
NOLT (definition), 1593
NOLT (notation), 1594
NOM (definition), 1595
NOM (notation), 1596
nonsingular
columns as basis
theorem CNMB, 1597
nonsingular matrices
linearly independent columns
theorem NMLIC, 1598
nonsingular matrix
Archetype B
example NM, 1599
column space, 1600
elemntary matrices
theorem NMPEM, 1601
equivalences
theorem NME1, 1602
theorem NME2, 1603
theorem NME3, 1604
theorem NME4, 1605
theorem NME5, 1606
theorem NME6, 1607
theorem NME7, 1608
theorem NME8, 1609
theorem NME9, 1610
matrix inverse, 1611
null space
example NSNM, 1612
nullity, 1613
product of nonsingular matrices
theorem NPNT, 1614
rank
theorem RNNM, 1615
row-reduced
theorem NMRRI, 1616
trivial null space
theorem NMTNS, 1617
unique solutions
theorem NMUS, 1618
nonsingular matrix, row-reduced
example NSR, 1619
norm
example CNSV, 1620
inner product, 1621
notation, 1622
notation
AM, 1623
C, 1624
CCCV, 1625
CCM, 1626
CCN, 1627
CNA, 1628
CNE, 1629
CNM, 1630
CSM, 1631
CV, 1632
CVA, 1633
CVC, 1634
CVE, 1635
CVSM, 1636
D, 1637
DM, 1638
DS, 1639
ELEM, 1640
ES, 1641
GES, 1642
IE, 1643
IM, 1644
IP, 1645
JB, 1646
KLT, 1647
LNS, 1648
LSMR, 1649
LT, 1650
LTR, 1651
M, 1652
MA, 1653
MC, 1654
ME, 1655
MI, 1656
MSM, 1657
MVP, 1658
NOLT, 1659
NOM, 1660
NSM, 1661
NV, 1662
RLT, 1663
RO, 1664
ROLT, 1665
ROM, 1666
RREFA, 1667
RSM, 1668
SC, 1669
SE, 1670
SETM, 1671
SI, 1672
SM, 1673
SSET, 1674
SSV, 1675
SU, 1676
TM, 1677
VSCV, 1678
VSM, 1679
ZCV, 1680
ZM, 1681
notation for a linear system
example NSE, 1682
NPNT (theorem), 1683
NRFO (subsection, section MR), 1684
NRREF (example), 1685
NS.MMA (computation, section MMA), 1686
NSAO (example), 1687
NSAQ (example), 1688
NSAQR (example), 1689
NSC2A (example), 1690
NSC2S (example), 1691
NSC2Z (example), 1692
NSDAT (example), 1693
NSDS (example), 1694
NSE (example), 1695
NSEAI (example), 1696
NSLE (example), 1697
NSLIL (example), 1698
NSM (definition), 1699
NSM (notation), 1700
NSM (subsection, section HSE), 1701
NSMS (theorem), 1702
NSNM (example), 1703
NSNM (subsection, section NM), 1704
NSR (example), 1705
NSS (example), 1706
NSSLI (subsection, section LI), 1707
Null space
as a span
example NSDS, 1708
null space
Archetype I
example NSEAI, 1709
basis
theorem BNS, 1710
computation
example CNS1, 1711
example CNS2, 1712
isomorphic to kernel, 1713
linearly independent basis
example LINSB, 1714
mathematica, 1715
matrix
definition NSM, 1716
nonsingular matrix, 1717
notation, 1718
singular matrix, 1719
spanning set
example SSNS, 1720
theorem SSNS, 1721
subspace
theorem NSMS, 1722
null space span, linearly independent
Archetype L
example NSLIL, 1723
nullity
computing, 1724
injective linear transformation
theorem NOILT, 1725
linear transformation
definition NOLT, 1726
matrix, 1727
definition NOM, 1728
notation, 1729, 1730
square matrix, 1731
NV (definition), 1732
NV (notation), 1733
O (archetype), 1734
O (Property), 1735
O (section), 1736
OBC (subsection, section B), 1737
OC (Property), 1738
OCN (Property), 1739
OD (subsection, section SD), 1740
OF (Property), 1741
OLTTR (example), 1742
OM (Property), 1743
one
column vectors
Property OC, 1744
complex numbers
Property OCN, 1745
field
Property OF, 1746
matrices
Property OM, 1747
vectors
Property O, 1748
ONFV (example), 1749
ONS (definition), 1750
ONTV (example), 1751
orthogonal
linear independence
theorem OSLI, 1752
set
example AOS, 1753
set of vectors
definition OSV, 1754
vector pairs
definition OV, 1755
orthogonal vectors
example TOV, 1756
orthonormal
definition ONS, 1757
matrix columns
example OSMC, 1758
orthonormal set
four vectors
example ONFV, 1759
three vectors
example ONTV, 1760
OSGMD (example), 1761
OSIS (theorem), 1762
OSLI (theorem), 1763
OSMC (example), 1764
OSV (definition), 1765
OV (definition), 1766
OV (subsection, section O), 1767
P (appendix), 1768
P (archetype), 1769
P (technique, section PT), 1770
particular solutions
example PSHS, 1771
PCNA (theorem), 1772
PCVS (example), 1773
PD (section), 1774
PDM (section), 1775
PEE (section), 1776
PEEF (theorem), 1777
PI (definition), 1778
PI (subsection, section LT), 1779
PI (technique, section PT), 1780
PIP (theorem), 1781
PM (example), 1782
PM (subsection, section EE), 1783
PMI (subsection, section MISLE), 1784
PMM (subsection, section MM), 1785
PMR (subsection, section MR), 1786
PNLT (subsection, section NLT), 1787
polynomial
of a matrix
example PM, 1788
polynomial vector space
dimension
theorem DP, 1789
practice
technique P, 1790
pre-image
definition PI, 1791
kernel
theorem KPI, 1792
pre-images
example SPIAS, 1793
Property
AA, 1794
AAC, 1795
AACN, 1796
AAF, 1797
AAM, 1798
AC, 1799
ACC, 1800
ACCN, 1801
ACF, 1802, 1803
ACM, 1804
AI, 1805
AIC, 1806
AICN, 1807
AIF, 1808
AIM, 1809
C, 1810
CC, 1811
CM, 1812
DCN, 1813
DF, 1814
DMAM, 1815
DSA, 1816
DSAC, 1817
DSAM, 1818
DVA, 1819
DVAC, 1820
MACN, 1821
MAF, 1822
MCCN, 1823
MCF, 1824, 1825
MICN, 1826
MIF, 1827
O, 1828
OC, 1829
OCN, 1830
OF, 1831
OM, 1832
SC, 1833
SCC, 1834
SCM, 1835
SMA, 1836
SMAC, 1837
SMAM, 1838
Z, 1839
ZC, 1840
ZCN, 1841
ZF, 1842
ZM, 1843
PSHS (example), 1844
PSHS (subsection, section LC), 1845
PSM (subsection, section SD), 1846
PSPHS (theorem), 1847
PSS (subsection, section SSLE), 1848
PSSD (theorem), 1849
PSSLS (theorem), 1850
PT (section), 1851
PTM (example), 1852
PTMEE (example), 1853
Q (archetype), 1854
R (archetype), 1855
R (chapter), 1856
range
full
example FRAN, 1857
isomorphic to column space
theorem RCSI, 1858
linear transformation
example RAO, 1859
notation, 1860
of a linear transformation
definition RLT, 1861
pre-image
theorem RPI, 1862
subspace
theorem RLTS, 1863
surjective linear transformation
theorem RSLT, 1864
via matrix representation
example RVMR, 1865
rank
computing
theorem CRN, 1866
linear transformation
definition ROLT, 1867
matrix
definition ROM, 1868
example RNM, 1869
notation, 1870, 1871
of transpose
example RRTI, 1872
square matrix
example RNSM, 1873
surjective linear transformation
theorem ROSLT, 1874
transpose
theorem RMRT, 1875
rank one decomposition
size 2
example ROD2, 1876
size 4
example ROD4, 1877
theorem ROD, 1878
rank+nullity
theorem RPNC, 1879
RAO (example), 1880
RCLS (theorem), 1881
RCSI (theorem), 1882
RD (subsection, section VS), 1883
RDS (theorem), 1884
READ (subsection, section B), 1885
READ (subsection, section CB), 1886
READ (subsection, section CRS), 1887
READ (subsection, section D), 1888
READ (subsection, section DM), 1889
READ (subsection, section EE), 1890
READ (subsection, section FS), 1891
READ (subsection, section HSE), 1892
READ (subsection, section ILT), 1893
READ (subsection, section IVLT), 1894
READ (subsection, section LC), 1895
READ (subsection, section LDS), 1896
READ (subsection, section LI), 1897
READ (subsection, section LISS), 1898
READ (subsection, section LT), 1899
READ (subsection, section MINM), 1900
READ (subsection, section MISLE), 1901
READ (subsection, section MM), 1902
READ (subsection, section MO), 1903
READ (subsection, section MR), 1904
READ (subsection, section NM), 1905
READ (subsection, section O), 1906
READ (subsection, section PD), 1907
READ (subsection, section PDM), 1908
READ (subsection, section PEE), 1909
READ (subsection, section RREF), 1910
READ (subsection, section S), 1911
READ (subsection, section SD), 1912
READ (subsection, section SLT), 1913
READ (subsection, section SS), 1914
READ (subsection, section SSLE), 1915
READ (subsection, section TSS), 1916
READ (subsection, section VO), 1917
READ (subsection, section VR), 1918
READ (subsection, section VS), 1919
READ (subsection, section WILA), 1920
reduced row-echelon form
analysis
notation, 1921
definition RREF, 1922
example NRREF, 1923
example RREF, 1924
extended
definition EEF, 1925
notation
example RREFN, 1926
unique
theorem RREFU, 1927
reducing a span
example RSC5, 1928
relation of linear dependence
definition RLD, 1929
definition RLDCV, 1930
REM (definition), 1931
REMEF (theorem), 1932
REMES (theorem), 1933
REMRS (theorem), 1934
RES (example), 1935
RGEN (theorem), 1936
RLD (definition), 1937
RLDCV (definition), 1938
RLT (definition), 1939
RLT (notation), 1940
RLT (subsection, section IS), 1941
RLT (subsection, section SLT), 1942
RLTS (theorem), 1943
RMRT (theorem), 1944
RNLT (subsection, section IVLT), 1945
RNM (example), 1946
RNM (subsection, section D), 1947
RNNM (subsection, section D), 1948
RNNM (theorem), 1949
RNSM (example), 1950
RO (definition), 1951
RO (notation), 1952
RO (subsection, section RREF), 1953
ROD (section), 1954
ROD (theorem), 1955
ROD2 (example), 1956
ROD4 (example), 1957
ROLT (definition), 1958
ROLT (notation), 1959
ROM (definition), 1960
ROM (notation), 1961
ROSLT (theorem), 1962
row operations
definition RO, 1963
elementary matrices, 1964, 1965
notation, 1966
row reduce
mathematica, 1967
ti83, 1968
ti86, 1969
row space
Archetype I
example RSAI, 1970
as column space, 1971
basis
example RSB, 1972
theorem BRS, 1973
matrix, 1974
notation, 1975
row-equivalent matrices
theorem REMRS, 1976
subspace
theorem RSMS, 1977
row-equivalent matrices
definition REM, 1978
example TREM, 1979
row space, 1980
row spaces
example RSREM, 1981
theorem REMES, 1982
row-reduce
the verb
definition RR, 1983
row-reduced matrices
theorem REMEF, 1984
RPI (theorem), 1985
RPNC (theorem), 1986
RPNDD (theorem), 1987
RR (definition), 1988
RR.MMA (computation, section MMA), 1989
RR.TI83 (computation, section TI83), 1990
RR.TI86 (computation, section TI86), 1991
RREF (definition), 1992
RREF (example), 1993
RREF (section), 1994
RREF (subsection, section RREF), 1995
RREFA (notation), 1996
RREFN (example), 1997
RREFU (theorem), 1998
RRTI (example), 1999
RS (example), 2000
RSAI (example), 2001
RSB (example), 2002
RSC5 (example), 2003
RSLT (theorem), 2004
RSM (definition), 2005
RSM (notation), 2006
RSM (subsection, section CRS), 2007
RSMS (theorem), 2008
RSNS (example), 2009
RSREM (example), 2010
RSSC4 (example), 2011
RT (subsection, section PD), 2012
RVMR (example), 2013
S (archetype), 2014
S (definition), 2015
S (example), 2016
S (section), 2017
SAA (example), 2018
SAB (example), 2019
SABMI (example), 2020
SAE (example), 2021
SAN (example), 2022
SAR (example), 2023
SAV (example), 2024
SC (definition), 2025
SC (example), 2026
SC (notation), 2027
SC (Property), 2028
SC (subsection, section S), 2029
SC (subsection, section SET), 2030
SC3 (example), 2031
SCAA (example), 2032
SCAB (example), 2033
SCAD (example), 2034
scalar closure
column vectors
Property SCC, 2035
matrices
Property SCM, 2036
vectors
Property SC, 2037
scalar multiple
matrix inverse, 2038
scalar multiplication
canceling scalars
theorem CSSM, 2039
canceling vectors
theorem CVSM, 2040
zero scalar
theorem ZSSM, 2041
zero vector
theorem ZVSM, 2042
zero vector result
theorem SMEZV, 2043
scalar multiplication associativity
column vectors
Property SMAC, 2044
matrices
Property SMAM, 2045
vectors
Property SMA, 2046
SCB (theorem), 2047
SCC (Property), 2048
SCM (Property), 2049
SD (section), 2050
SDS (example), 2051
SE (definition), 2052
SE (notation), 2053
SEE (example), 2054
SEEF (example), 2055
SER (theorem), 2056
set
cardinality
definition C, 2057
example CS, 2058
notation, 2059
complement
definition SC, 2060
example SC, 2061
notation, 2062
definition SET, 2063
empty
definition ES, 2064
equality
definition SE, 2065
notation, 2066
intersection
definition SI, 2067
example SI, 2068
notation, 2069
membership
example SETM, 2070
notation, 2071
size, 2072
subset, 2073
union
definition SU, 2074
example SU, 2075
notation, 2076
SET (definition), 2077
SET (section), 2078
SETM (example), 2079
SETM (notation), 2080
shoes, 2081
SHS (subsection, section HSE), 2082
SI (definition), 2083
SI (example), 2084
SI (notation), 2085
SI (subsection, section IVLT), 2086
SIM (definition), 2087
similar matrices
equal eigenvalues
example EENS, 2088
eual eigenvalues
theorem SMEE, 2089
example SMS3, 2090
example SMS5, 2091
similarity
definition SIM, 2092
equivalence relation
theorem SER, 2093
singular matrix
Archetype A
example S, 2094
null space
example NSS, 2095
singular matrix, row-reduced
example SRR, 2096
SLE (chapter), 2097
SLE (definition), 2098
SLE (subsection, section SSLE), 2099
SLELT (subsection, section IVLT), 2100
SLEMM (theorem), 2101
SLSLC (theorem), 2102
SLT (definition), 2103
SLT (section), 2104
SLTB (theorem), 2105
SLTD (subsection, section SLT), 2106
SLTD (theorem), 2107
SLTLT (theorem), 2108
SM (definition), 2109
SM (notation), 2110
SM (subsection, section SD), 2111
SM2Z7 (example), 2112
SM32 (example), 2113
SMA (Property), 2114
SMAC (Property), 2115
SMAM (Property), 2116
SMEE (theorem), 2117
SMEZV (theorem), 2118
SMLT (example), 2119
SMS (theorem), 2120
SMS3 (example), 2121
SMS5 (example), 2122
SMZD (theorem), 2123
SMZE (theorem), 2124
SNCM (theorem), 2125
SO (subsection, section SET), 2126
socks, 2127
SOL (subsection, section B), 2128
SOL (subsection, section CB), 2129
SOL (subsection, section CRS), 2130
SOL (subsection, section D), 2131
SOL (subsection, section DM), 2132
SOL (subsection, section EE), 2133
SOL (subsection, section F), 2134
SOL (subsection, section FS), 2135
SOL (subsection, section HSE), 2136
SOL (subsection, section ILT), 2137
SOL (subsection, section IVLT), 2138
SOL (subsection, section LC), 2139
SOL (subsection, section LDS), 2140
SOL (subsection, section LI), 2141
SOL (subsection, section LISS), 2142
SOL (subsection, section LT), 2143
SOL (subsection, section MINM), 2144
SOL (subsection, section MISLE), 2145
SOL (subsection, section MM), 2146
SOL (subsection, section MO), 2147
SOL (subsection, section MR), 2148
SOL (subsection, section NM), 2149
SOL (subsection, section PD), 2150
SOL (subsection, section PDM), 2151
SOL (subsection, section PEE), 2152
SOL (subsection, section RREF), 2153
SOL (subsection, section S), 2154
SOL (subsection, section SD), 2155
SOL (subsection, section SLT), 2156
SOL (subsection, section SS), 2157
SOL (subsection, section SSLE), 2158
SOL (subsection, section TSS), 2159
SOL (subsection, section VO), 2160
SOL (subsection, section VR), 2161
SOL (subsection, section WILA), 2162
solution set
Archetype A
example SAA, 2163
archetype E
example SAE, 2164
theorem PSPHS, 2165
solution sets
possibilities
theorem PSSLS, 2166
solution vector
definition SV, 2167
solving homogeneous system
Archetype A
example HISAA, 2168
Archetype B
example HUSAB, 2169
Archetype D
example HISAD, 2170
solving nonlinear equations
example STNE, 2171
SP4 (example), 2172
span
basic
example ABS, 2173
basis
theorem BS, 2174
definition SS, 2175
definition SSCV, 2176
improved
example IAS, 2177
notation, 2178
reducing
example RSSC4, 2179
reduction
example RS, 2180
removing vectors
example COV, 2181
reworking elements
example RES, 2182
set of polynomials
example SSP, 2183
subspace
theorem SSS, 2184
span of columns
Archetype A
example SCAA, 2185
Archetype B
example SCAB, 2186
Archetype D
example SCAD, 2187
spanning set
crazy vector space
example SSC, 2188
definition TSVS, 2189
matrices
example SSM22, 2190
more vectors
theorem SSLD, 2191
polynomials
example SSP4, 2192
SPIAS (example), 2193
SQM (definition), 2194
SRR (example), 2195
SS (definition), 2196
SS (example), 2197
SS (section), 2198
SS (subsection, section LISS), 2199
SS (theorem), 2200
SSC (example), 2201
SSCV (definition), 2202
SSET (definition), 2203
SSET (example), 2204
SSET (notation), 2205
SSLD (theorem), 2206
SSLE (section), 2207
SSM22 (example), 2208
SSNS (example), 2209
SSNS (subsection, section SS), 2210
SSNS (theorem), 2211
SSP (example), 2212
SSP4 (example), 2213
SSRLT (theorem), 2214
SSS (theorem), 2215
SSSLT (subsection, section SLT), 2216
SSV (notation), 2217
SSV (subsection, section SS), 2218
starting proofs
technique GS, 2219
STLT (example), 2220
STNE (example), 2221
SU (definition), 2222
SU (example), 2223
SU (notation), 2224
submatrix
notation, 2225
subset
definition SSET, 2226
notation, 2227
subspace
as null space
example RSNS, 2228
characterized
example ASC, 2229
definition S, 2230
in
example SP4, 2231
not, additive closure
example NSC2A, 2232
not, scalar closure
example NSC2S, 2233
not, zero vector
example NSC2Z, 2234
testing
theorem TSS, 2235
trivial
definition TS, 2236
verification
example SC3, 2237
example SM32, 2238
subspaces
equal dimension
theorem EDYES, 2239
surjective
Archetype N
example SAN, 2240
example SAR, 2241
not
example NSAQ, 2242
example NSAQR, 2243
not, Archetype O
example NSAO, 2244
not, by dimension
example NSDAT, 2245
polynomials to matrices
example SAV, 2246
surjective linear transformation
bases
theorem SLTB, 2247
surjective linear transformations
dimension
theorem SLTD, 2248
SUV (definition), 2249
SUVB (theorem), 2250
SUVOS (example), 2251
SV (definition), 2252
SVP4 (example), 2253
SYM (definition), 2254
SYM (example), 2255
symmetric matrices
theorem SMS, 2256
symmetric matrix
example SYM, 2257
system of equations
vector equality
example VESE, 2258
system of linear equations
definition SLE, 2259
T (archetype), 2260
T (part), 2261
T (technique, section PT), 2262
TCSD (example), 2263
technique
C, 2264
CD, 2265
CP, 2266
CV, 2267
D, 2268
DC, 2269
E, 2270
GS, 2271
I, 2272
L, 2273
LC, 2274
ME, 2275
N, 2276
P, 2277
PI, 2278
T, 2279
U, 2280
theorem
AISM, 2281
AIU, 2282
BCS, 2283
BIS, 2284
BNS, 2285
BRS, 2286
BS, 2287
CB, 2288
CCRA, 2289
CCRM, 2290
CCT, 2291
CFDVS, 2292
CFNLT, 2293
CHT, 2294
CILTI, 2295
CINM, 2296
CIVLT, 2297
CLI, 2298
CLTLT, 2299
CMVEI, 2300
CNMB, 2301
COB, 2302
CRMA, 2303
CRMSM, 2304
CRN, 2305
CRSM, 2306
CRVA, 2307
CSCS, 2308
CSLTS, 2309
CSMS, 2310
CSNM, 2311
CSRN, 2312
CSRST, 2313
CSS, 2314
CSSM, 2315
CUMOS, 2316
CVSM, 2317
DC, 2318
DCM, 2319
DCP, 2320
DEC, 2321
DED, 2322
DEM, 2323
DEMMM, 2324
DER, 2325
DERC, 2326
DFS, 2327
DGES, 2328
DIM, 2329
DLDS, 2330
DM, 2331
DMFE, 2332
DMST, 2333
DNLT, 2334
DP, 2335
DRCM, 2336
DRCMA, 2337
DRCS, 2338
DRMM, 2339
DSD, 2340
DSFB, 2341
DSFOS, 2342
DSLI, 2343
DSZI, 2344
DSZV, 2345
DT, 2346
DZRC, 2347
EDELI, 2348
EDYES, 2349
EER, 2350
EIM, 2351
EIS, 2352
ELIS, 2353
EMDRO, 2354
EMHE, 2355
EMMVP, 2356
EMN, 2357
EMNS, 2358
EMP, 2359
EMRCP, 2360
EMS, 2361
ENLT, 2362
EOMP, 2363
EOPSS, 2364
EPM, 2365
ERMCP, 2366
ESMM, 2367
ETM, 2368
FIMP, 2369
FS, 2370
FTMR, 2371
FVCS, 2372
G, 2373
GEK, 2374
GESD, 2375
GESIS, 2376
GSPCV, 2377
HMOE, 2378
HMRE, 2379
HMVEI, 2380
HSC, 2381
ICBM, 2382
ICLT, 2383
IFDVS, 2384
IILT, 2385
ILTB, 2386
ILTD, 2387
ILTIS, 2388
ILTLI, 2389
ILTLT, 2390
IMILT, 2391
IMR, 2392
IPAC, 2393
IPN, 2394
IPSM, 2395
IPVA, 2396
ISRN, 2397
IVSED, 2398
JCFLT, 2399
KILT, 2400
KLTS, 2401
KNSI, 2402
KPI, 2403
KPIS, 2404
KPLT, 2405
KPNLT, 2406
LIVHS, 2407
LIVRN, 2408
LNSMS, 2409
LTDB, 2410
LTLC, 2411
LTTZZ, 2412
MBLT, 2413
MCT, 2414
ME, 2415
MIMI, 2416
MISM, 2417
MIT, 2418
MIU, 2419
MLTCV, 2420
MLTLT, 2421
MMA, 2422
MMCC, 2423
MMDAA, 2424
MMIM, 2425
MMIP, 2426
MMSMM, 2427
MMT, 2428
MMZM, 2429
MNEM, 2430
MRCB, 2431
MRCLT, 2432
MRMLT, 2433
MRRGE, 2434
MRSLT, 2435
MVSLD, 2436
NEM, 2437
NI, 2438
NJB, 2439
NME1, 2440
NME2, 2441
NME3, 2442
NME4, 2443
NME5, 2444
NME6, 2445
NME7, 2446
NME8, 2447
NME9, 2448
NMLIC, 2449
NMPEM, 2450
NMRRI, 2451
NMTNS, 2452
NMUS, 2453
NOILT, 2454
NPNT, 2455
NSMS, 2456
OSIS, 2457
OSLI, 2458
PCNA, 2459
PEEF, 2460
PIP, 2461
PSPHS, 2462
PSSD, 2463
PSSLS, 2464
RCLS, 2465
RCSI, 2466
RDS, 2467
REMEF, 2468
REMES, 2469
REMRS, 2470
RGEN, 2471
RLTS, 2472
RMRT, 2473
RNNM, 2474
ROD, 2475
ROSLT, 2476
RPI, 2477
RPNC, 2478
RPNDD, 2479
RREFU, 2480
RSLT, 2481
RSMS, 2482
SCB, 2483
SER, 2484
SLEMM, 2485
SLSLC, 2486
SLTB, 2487
SLTD, 2488
SLTLT, 2489
SMEE, 2490
SMEZV, 2491
SMS, 2492
SMZD, 2493
SMZE, 2494
SNCM, 2495
SS, 2496
SSLD, 2497
SSNS, 2498
SSRLT, 2499
SSS, 2500
SUVB, 2501
technique T, 2502
TMA, 2503
TMSM, 2504
TSS, 2505
TT, 2506
TTMI, 2507
UMI, 2508
UMPIP, 2509
UTMR, 2510
VAC, 2511
VFSLS, 2512
VRI, 2513
VRILT, 2514
VRLT, 2515
VRRB, 2516
VRS, 2517
VSLT, 2518
VSPCV, 2519
VSPM, 2520
ZSSM, 2521
ZVSM, 2522
ZVU, 2523
ti83
matrix entry (computation), 2524
row reduce (computation), 2525
vector linear combinations (computation), 2526
TI83 (section), 2527
ti86
matrix entry (computation), 2528
row reduce (computation), 2529
transpose of a matrix (computation), 2530
vector linear combinations (computation), 2531
TI86 (section), 2532
TIS (example), 2533
TIVS (example), 2534
TKAP (example), 2535
TLC (example), 2536
TM (definition), 2537
TM (example), 2538
TM (notation), 2539
TM.MMA (computation, section MMA), 2540
TM.TI86 (computation, section TI86), 2541
TMA (theorem), 2542
TMP (example), 2543
TMSM (theorem), 2544
TOV (example), 2545
trail mix
example TMP, 2546
transpose
matrix scalar multiplication
theorem TMSM, 2547
example TM, 2548
matrix addition
theorem TMA, 2549
matrix inverse, 2550, 2551
notation, 2552
scalar multiplication, 2553
transpose of a matrix
mathematica, 2554
ti86, 2555
transpose of a transpose
theorem TT, 2556
TREM (example), 2557
trivial solution
system of equations
definition TSHSE, 2558
TS (definition), 2559
TS (subsection, section S), 2560
TSHSE (definition), 2561
TSM (subsection, section MO), 2562
TSS (section), 2563
TSS (subsection, section S), 2564
TSS (theorem), 2565
TSVS (definition), 2566
TT (theorem), 2567
TTMI (theorem), 2568
TTS (example), 2569
typical systems,
example TTS, 2570
U (archetype), 2571
U (technique, section PT), 2572
UM (definition), 2573
UM (subsection, section MINM), 2574
UM3 (example), 2575
UMI (theorem), 2576
UMPIP (theorem), 2577
unique solution,
example US, 2578
example USR, 2579
uniqueness
technique U, 2580
unit vectors
basis
theorem SUVB, 2581
definition SUV, 2582
orthogonal
example SUVOS, 2583
unitary
permutation matrix
example UPM, 2584
size 3
example UM3, 2585
unitary matrices
columns
theorem CUMOS, 2586
unitary matrix
inner product
theorem UMPIP, 2587
UPM (example), 2588
URREF (subsection, section LC), 2589
US (example), 2590
USR (example), 2591
UTMR (subsection, section JCF), 2592
UTMR (theorem), 2593
V (archetype), 2594
V (chapter), 2595
VA (example), 2596
VAC (theorem), 2597
VEASM (subsection, section VO), 2598
vector
addition
definition CVA, 2599
column
definition CV, 2600
equality
definition CVE, 2601
notation, 2602
inner product
definition IP, 2603
norm
definition NV, 2604
notation, 2605
of constants
definition VOC, 2606
product with matrix, 2607, 2608
scalar multiplication
definition CVSM, 2609
vector addition
example VA, 2610
vector component
notation, 2611
vector form of solutions
Archetype D
example VFSAD, 2612
Archetype I
example VFSAI, 2613
Archetype L
example VFSAL, 2614
example VFS, 2615
mathematica, 2616
theorem VFSLS, 2617
vector linear combinations
mathematica, 2618
ti83, 2619
ti86, 2620
vector representation
example AVR, 2621
example VRC4, 2622
injective
theorem VRI, 2623
invertible
theorem VRILT, 2624
linear transformation
definition VR, 2625
theorem VRLT, 2626
surjective
theorem VRS, 2627
theorem VRRB, 2628
vector representations
polynomials
example VRP2, 2629
vector scalar multiplication
example CVSM, 2630
vector space
characterization
theorem CFDVS, 2631
column vectors
definition VSCV, 2632
definition VS, 2633
infinite dimension
example VSPUD, 2634
linear transformations
theorem VSLT, 2635
over integers mod 5
example VSIM5, 2636
vector space of column vectors
notation, 2637
vector space of functions
example VSF, 2638
vector space of infinite sequences
example VSIS, 2639
vector space of matrices
definition VSM, 2640
example VSM, 2641
notation, 2642
vector space of polynomials
example VSP, 2643
vector space properties
column vectors
theorem VSPCV, 2644
matrices
theorem VSPM, 2645
vector space, crazy
example CVS, 2646
vector space, singleton
example VSS, 2647
vector spaces
isomorphic
definition IVS, 2648
theorem IFDVS, 2649
VESE (example), 2650
VFS (example), 2651
VFSAD (example), 2652
VFSAI (example), 2653
VFSAL (example), 2654
VFSLS (theorem), 2655
VFSS (subsection, section LC), 2656
VFSS.MMA (computation, section MMA), 2657
VLC.MMA (computation, section MMA), 2658
VLC.TI83 (computation, section TI83), 2659
VLC.TI86 (computation, section TI86), 2660
VO (section), 2661
VOC (definition), 2662
VR (definition), 2663
VR (section), 2664
VR (subsection, section LISS), 2665
VRC4 (example), 2666
VRI (theorem), 2667
VRILT (theorem), 2668
VRLT (theorem), 2669
VRP2 (example), 2670
VRRB (theorem), 2671
VRS (theorem), 2672
VS (chapter), 2673
VS (definition), 2674
VS (section), 2675
VS (subsection, section VS), 2676
VSCV (definition), 2677
VSCV (example), 2678
VSCV (notation), 2679
VSF (example), 2680
VSIM5 (example), 2681
VSIS (example), 2682
VSLT (theorem), 2683
VSM (definition), 2684
VSM (example), 2685
VSM (notation), 2686
VSP (example), 2687
VSP (subsection, section MO), 2688
VSP (subsection, section VO), 2689
VSP (subsection, section VS), 2690
VSPCV (theorem), 2691
VSPM (theorem), 2692
VSPUD (example), 2693
VSS (example), 2694
W (archetype), 2695
WILA (section), 2696
X (archetype), 2697
Z (Property), 2698
ZC (Property), 2699
ZCN (Property), 2700
ZCV (definition), 2701
ZCV (notation), 2702
zero
complex numbers
Property ZCN, 2703
field
Property ZF, 2704
zero column vector
definition ZCV, 2705
notation, 2706
zero matrix
notation, 2707
zero vector
column vectors
Property ZC, 2708
matrices
Property ZM, 2709
unique
theorem ZVU, 2710
vectors
Property Z, 2711
ZF (Property), 2712
ZM (definition), 2713
ZM (notation), 2714
ZM (Property), 2715
ZNDAB (example), 2716
ZSSM (theorem), 2717
ZVSM (theorem), 2718
ZVU (theorem), 2719