B (archetype), 97
B (definition), 98
B (section), 99
B (subsection, section B), 100
basis
columns nonsingular matrix
example CABAK, 101
common size
theorem BIS, 102
crazy vector apace
example BC, 103
definition B, 104
matrices
example BM, 105
example BSM22, 106
polynomials
example BP, 107
example BPR, 108
example BSP4, 109
example SVP4, 110
subspace of matrices
example BDM22, 111
BC (example), 112
BCS (theorem), 113
BDE (example), 114
BDM22 (example), 115
best cities
money magazine
example MBC, 116
BIS (theorem), 117
BM (example), 118
BNM (subsection, section B), 119
BNS (theorem), 120
BP (example), 121
BPR (example), 122
BRLT (example), 123
BRS (theorem), 124
BS (theorem), 125
BSCV (subsection, section B), 126
BSM22 (example), 127
BSP4 (example), 128
C (archetype), 129
C (definition), 130
C (notation), 131
C (part), 132
C (Property), 133
C (technique, section PT), 134
CABAK (example), 135
CACN (Property), 136
CAEHW (example), 137
CAF (Property), 138
canonical form
nilpotent linear transformation
example CFNLT, 139
theorem CFNLT, 140
CAV (subsection, section O), 141
Cayley-Hamilton
theorem CHT, 142
CB (section), 143
CB (theorem), 144
CBCV (example), 145
CBM (definition), 146
CBM (subsection, section CB), 147
CBP (example), 148
CC (Property), 149
CCCV (definition), 150
CCCV (notation), 151
CCM (definition), 152
CCM (example), 153
CCM (notation), 154
CCM (theorem), 155
CCN (definition), 156
CCN (notation), 157
CCN (subsection, section CNO), 158
CCRA (theorem), 159
CCRM (theorem), 160
CCT (theorem), 161
CD (subsection, section DM), 162
CD (technique, section PT), 163
CEE (subsection, section EE), 164
CELT (example), 165
CELT (subsection, section CB), 166
CEMS6 (example), 167
CF (section), 168
CFDVS (theorem), 169
CFNLT (example), 170
CFNLT (subsection, section NLT), 171
CFNLT (theorem), 172
CFV (example), 173
change of basis
between polynomials
example CBP, 174
change-of-basis
between column vectors
example CBCV, 175
matrix representation
theorem MRCB, 176
similarity
theorem SCB, 177
theorem CB, 178
change-of-basis matrix
definition CBM, 179
inverse
theorem ICBM, 180
characteristic polynomial
definition CP, 181
degree
theorem DCP, 182
size 3 matrix
example CPMS3, 183
CHT (subsection, section JCF), 184
CHT (theorem), 185
CILT (subsection, section ILT), 186
CILTI (theorem), 187
CIM (subsection, section MISLE), 188
CINM (theorem), 189
CIVLT (example), 190
CIVLT (theorem), 191
CLI (theorem), 192
CLTLT (theorem), 193
CM (definition), 194
CM (Property), 195
CM32 (example), 196
CMCN (Property), 197
CMF (Property), 198
CMI (example), 199
CMIAB (example), 200
CMVEI (theorem), 201
CN (appendix), 202
CNA (definition), 203
CNA (notation), 204
CNA (subsection, section CNO), 205
CNE (definition), 206
CNE (notation), 207
CNM (definition), 208
CNM (notation), 209
CNMB (theorem), 210
CNO (section), 211
CNS1 (example), 212
CNS2 (example), 213
CNSV (example), 214
COB (theorem), 215
coefficient matrix
definition CM, 216
nonsingular
theorem SNCM, 217
column space
as null space
theorem FS, 218
Archetype A
example CSAA, 219
Archetype B
example CSAB, 220
as null space
example CSANS, 221
as null space, Archetype G
example FSAG, 222
as row space
theorem CSRST, 223
basis
theorem BCS, 224
consistent system
theorem CSCS, 225
consistent systems
example CSMCS, 226
isomorphic to range, 227
matrix, 228
nonsingular matrix
theorem CSNM, 229
notation, 230
original columns, Archetype D
example CSOCD, 231
row operations, Archetype I
example CSROI, 232
subspace
theorem CSMS, 233
testing membership
example MCSM, 234
two computations
example CSTW, 235
column vector addition
notation, 236
column vector scalar multiplication
notation, 237
commutativity
column vectors
Property CC, 238
matrices
Property CM, 239
vectors
Property C, 240
complex -space
example VSCV, 241
complex arithmetic
example ACN, 242
complex number
conjugate
example CSCN, 243
modulus
example MSCN, 244
complex number
conjugate
definition CCN, 245
modulus
definition MCN, 246
complex numbers
addition
definition CNA, 247
notation, 248
arithmetic properties
theorem PCNA, 249
equality
definition CNE, 250
notation, 251
multiplication
definition CNM, 252
notation, 253
complex vector space
dimension
theorem DCM, 254
composition
injective linear transformations
theorem CILTI, 255
surjective linear transformations
theorem CSLTS, 256
conjugate
addition
theorem CCRA, 257
column vector
definition CCCV, 258
matrix
definition CCM, 259
notation, 260
multiplication
theorem CCRM, 261
notation, 262
of conjugate of a matrix
theorem CCM, 263
scalar multiplication
theorem CRSM, 264
twice
theorem CCT, 265
vector addition
theorem CRVA, 266
conjugate of a vector
notation, 267
conjugation
matrix addition
theorem CRMA, 268
matrix scalar multiplication
theorem CRMSM, 269
matrix transpose
theorem MCT, 270
consistent linear system, 271
consistent linear systems
theorem CSRN, 272
consistent system
definition CS, 273
constructive proofs
technique C, 274
contradiction
technique CD, 275
contrapositive
technique CP, 276
converse
technique CV, 277
coordinates
orthonormal basis
theorem COB, 278
coordinatization
linear combination of matrices
example CM32, 279
linear independence
theorem CLI, 280
orthonormal basis
example CROB3, 281
example CROB4, 282
spanning sets
theorem CSS, 283
coordinatization principle, 284
coordinatizing
polynomials
example CP2, 285
COV (example), 286
COV (subsection, section LDS), 287
CP (definition), 288
CP (subsection, section VR), 289
CP (technique, section PT), 290
CP2 (example), 291
CPMS3 (example), 292
CPSM (theorem), 293
crazy vector space
example CVSR, 294
properties
example PCVS, 295
CRMA (theorem), 296
CRMSM (theorem), 297
CRN (theorem), 298
CROB3 (example), 299
CROB4 (example), 300
CRS (section), 301
CRS (subsection, section FS), 302
CRSM (theorem), 303
CRVA (theorem), 304
CS (definition), 305
CS (example), 306
CS (subsection, section TSS), 307
CSAA (example), 308
CSAB (example), 309
CSANS (example), 310
CSCN (example), 311
CSCS (theorem), 312
CSIP (example), 313
CSLT (subsection, section SLT), 314
CSLTS (theorem), 315
CSM (definition), 316
CSM (notation), 317
CSMCS (example), 318
CSMS (theorem), 319
CSNM (subsection, section CRS), 320
CSNM (theorem), 321
CSOCD (example), 322
CSRN (theorem), 323
CSROI (example), 324
CSRST (figure), 325
CSRST (theorem), 326
CSS (theorem), 327
CSSE (subsection, section CRS), 328
CSSOC (subsection, section CRS), 329
CSTW (example), 330
CTD (subsection, section TD), 331
CTLT (example), 332
CUMOS (theorem), 333
curve fitting
polynomial through 5 points
example PTFP, 334
CV (definition), 335
CV (notation), 336
CV (technique, section PT), 337
CVA (definition), 338
CVA (notation), 339
CVC (notation), 340
CVE (definition), 341
CVE (notation), 342
CVS (example), 343
CVS (subsection, section VR), 344
CVSM (definition), 345
CVSM (example), 346
CVSM (notation), 347
CVSR (example), 348
D (acronyms, section PDM), 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
LSMR, 430
LSS, 431
LT, 432
LTA, 433
LTC, 434
LTM, 435
LTR, 436
LTSM, 437
M, 438
MA, 439
MCN, 440
ME, 441
MI, 442
MM, 443
MR, 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
SU, 484
SUV, 485
SV, 486
SYM, 487
T, 488
technique D, 489
TM, 490
TS, 491
TSHSE, 492
TSVS, 493
UM, 494
UTM, 495
VM, 496
VOC, 497
VR, 498
VS, 499
VSCV, 500
VSM, 501
ZCV, 502
ZM, 503
DEHD (example), 504
DEM (theorem), 505
DEMMM (theorem), 506
DEMS5 (example), 507
DER (theorem), 508
DERC (theorem), 509
determinant
computed two ways
example TCSD, 510
definition DM, 511
equal rows or columns
theorem DERC, 512
expansion, columns
theorem DEC, 513
expansion, rows
theorem DER, 514
identity matrix
theorem DIM, 515
matrix multiplication
theorem DRMM, 516
nonsingular matrix, 517
notation, 518
row or column multiple
theorem DRCM, 519
row or column swap
theorem DRCS, 520
size 2 matrix
theorem DMST, 521
size 3 matrix
example D33M, 522
transpose
theorem DT, 523
via row operations
example DRO, 524
zero
theorem SMZD, 525
zero row or column
theorem DZRC, 526
zero versus nonzero
example ZNDAB, 527
determinant, upper triangular matrix
example DUTM, 528
determinants
elementary matrices
theorem DEMMM, 529
DF (Property), 530
DF (subsection, section CF), 531
DFS (subsection, section PD), 532
DFS (theorem), 533
DGES (theorem), 534
diagonal matrix
definition DIM, 535
diagonalizable
definition DZM, 536
distinct eigenvalues
example DEHD, 537
theorem DED, 538
full eigenspaces
theorem DMFE, 539
not
example NDMS4, 540
diagonalizable matrix
high power
example HPDM, 541
diagonalization
Archetype B
example DAB, 542
criteria
theorem DC, 543
example DMS3, 544
DIM (definition), 545
DIM (theorem), 546
dimension
crazy vector space
example DC, 547
definition D, 548
notation, 549
polynomial subspace
example DSP4, 550
proper subspaces
theorem PSSD, 551
subspace
example DSM22, 552
direct sum
decomposing zero vector
theorem DSZV, 553
definition DS, 554
dimension
theorem DSD, 555
example SDS, 556
from a basis
theorem DSFB, 557
from one subspace
theorem DSFOS, 558
notation, 559
zero intersection
theorem DSZI, 560
direct sums
linear independence
theorem DSLI, 561
repeated
theorem RDS, 562
distributivity
complex numbers
Property DCN, 563
field
Property DF, 564
distributivity, matrix addition
matrices
Property DMAM, 565
distributivity, scalar addition
column vectors
Property DSAC, 566
matrices
Property DSAM, 567
vectors
Property DSA, 568
distributivity, vector addition
column vectors
Property DVAC, 569
vectors
Property DVA, 570
DLDS (theorem), 571
DLTA (figure), 572
DLTM (figure), 573
DM (definition), 574
DM (notation), 575
DM (section), 576
DM (theorem), 577
DMAM (Property), 578
DMFE (theorem), 579
DMHP (subsection, section HP), 580
DMHP (theorem), 581
DMMP (theorem), 582
DMS3 (example), 583
DMST (theorem), 584
DNLT (theorem), 585
DNMMM (subsection, section PDM), 586
DP (theorem), 587
DRCM (theorem), 588
DRCMA (theorem), 589
DRCS (theorem), 590
DRMM (theorem), 591
DRO (example), 592
DRO (subsection, section PDM), 593
DROEM (subsection, section PDM), 594
DS (definition), 595
DS (notation), 596
DS (subsection, section PD), 597
DSA (Property), 598
DSAC (Property), 599
DSAM (Property), 600
DSD (theorem), 601
DSFB (theorem), 602
DSFOS (theorem), 603
DSLI (theorem), 604
DSM22 (example), 605
DSP4 (example), 606
DSZI (theorem), 607
DSZV (theorem), 608
DT (theorem), 609
DTSLS (figure), 610
DUTM (example), 611
DVA (Property), 612
DVAC (Property), 613
DVM (theorem), 614
DVS (subsection, section D), 615
DZM (definition), 616
DZRC (theorem), 617
E (acronyms, section SD), 618
E (archetype), 619
E (chapter), 620
E (technique, section PT), 621
ECEE (subsection, section EE), 622
EDELI (theorem), 623
EDYES (theorem), 624
EE (section), 625
EEE (subsection, section EE), 626
EEF (definition), 627
EEF (subsection, section FS), 628
EELT (definition), 629
EELT (subsection, section CB), 630
EEM (definition), 631
EEM (subsection, section EE), 632
EEMAP (theorem), 633
EENS (example), 634
EER (theorem), 635
EESR (theorem), 636
EHM (subsection, section PEE), 637
eigenspace
as null space
theorem EMNS, 638
definition EM, 639
invariant subspace
theorem EIS, 640
subspace
theorem EMS, 641
eigenvalue
algebraic multiplicity
definition AME, 642
complex
example CEMS6, 643
definition EEM, 644
existence
example CAEHW, 645
theorem EMHE, 646
geometric multiplicity
definition GME, 647
index, 648
linear transformation
definition EELT, 649
multiplicities
example EMMS4, 650
power
theorem EOMP, 651
root of characteristic polynomial
theorem EMRCP, 652
scalar multiple
theorem ESMM, 653
symmetric matrix
example ESMS4, 654
zero
theorem SMZE, 655
eigenvalues
building desired
example BDE, 656
complex, of a linear transformation
example CELT, 657
conjugate pairs
theorem ERMCP, 658
distinct
example DEMS5, 659
example SEE, 660
Hermitian matrices
theorem HMRE, 661
inverse
theorem EIM, 662
maximum number
theorem MNEM, 663
multiplicities
example HMEM5, 664
theorem ME, 665
number
theorem NEM, 666
of a polynomial
theorem EPM, 667
size 3 matrix
example EMS3, 668
example ESMS3, 669
transpose
theorem ETM, 670
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 671
eigenvector, 672
linear transformation, 673
eigenvectors, 674
conjugate pairs, 675
Hermitian matrices
theorem HMOE, 676
linear transformation
example ELTBM, 677
example ELTBP, 678
linearly independent
theorem EDELI, 679
of a linear transformation
example ELTT, 680
EILT (subsection, section ILT), 681
EIM (theorem), 682
EIS (example), 683
EIS (theorem), 684
ELEM (definition), 685
ELEM (notation), 686
elementary matrices
definition ELEM, 687
determinants
theorem DEM, 688
nonsingular
theorem EMN, 689
notation, 690
row operations
example EMRO, 691
theorem EMDRO, 692
ELIS (theorem), 693
ELTBM (example), 694
ELTBP (example), 695
ELTT (example), 696
EM (definition), 697
EM (subsection, section DM), 698
EMDRO (theorem), 699
EMHE (theorem), 700
EMMS4 (example), 701
EMMVP (theorem), 702
EMN (theorem), 703
EMNS (theorem), 704
EMP (theorem), 705
empty set, 706
notation, 707
EMRCP (theorem), 708
EMRO (example), 709
EMS (theorem), 710
EMS3 (example), 711
ENLT (theorem), 712
EO (definition), 713
EOMP (theorem), 714
EOPSS (theorem), 715
EPM (theorem), 716
EPSM (theorem), 717
equal matrices
via equal matrix-vector products
theorem EMMVP, 718
equation operations
definition EO, 719
theorem EOPSS, 720
equivalence statements
technique E, 721
equivalences
technique ME, 722
equivalent systems
definition ESYS, 723
ERMCP (theorem), 724
ES (definition), 725
ES (notation), 726
ESEO (subsection, section SSLE), 727
ESLT (subsection, section SLT), 728
ESMM (theorem), 729
ESMS3 (example), 730
ESMS4 (example), 731
ESYS (definition), 732
ETM (theorem), 733
EVS (subsection, section VS), 734
example
AALC, 735
ABLC, 736
ABS, 737
ACN, 738
AHSAC, 739
AIVLT, 740
ALT, 741
ALTMM, 742
AM, 743
AMAA, 744
ANILT, 745
ANM, 746
AOS, 747
ASC, 748
AVR, 749
BC, 750
BDE, 751
BDM22, 752
BM, 753
BP, 754
BPR, 755
BRLT, 756
BSM22, 757
BSP4, 758
CABAK, 759
CAEHW, 760
CBCV, 761
CBP, 762
CCM, 763
CELT, 764
CEMS6, 765
CFNLT, 766
CFV, 767
CIVLT, 768
CM32, 769
CMI, 770
CMIAB, 771
CNS1, 772
CNS2, 773
CNSV, 774
COV, 775
CP2, 776
CPMS3, 777
CROB3, 778
CROB4, 779
CS, 780
CSAA, 781
CSAB, 782
CSANS, 783
CSCN, 784
CSIP, 785
CSMCS, 786
CSOCD, 787
CSROI, 788
CSTW, 789
CTLT, 790
CVS, 791
CVSM, 792
CVSR, 793
D33M, 794
DAB, 795
DC, 796
DEHD, 797
DEMS5, 798
DMS3, 799
DRO, 800
DSM22, 801
DSP4, 802
DUTM, 803
EENS, 804
EIS, 805
ELTBM, 806
ELTBP, 807
ELTT, 808
EMMS4, 809
EMRO, 810
EMS3, 811
ESMS3, 812
ESMS4, 813
FDV, 814
FF8, 815
FRAN, 816
FS1, 817
FS2, 818
FSAG, 819
FSCF, 820
GE4, 821
GE6, 822
GENR6, 823
GSTV, 824
HISAA, 825
HISAD, 826
HMEM5, 827
HP, 828
HPDM, 829
HUSAB, 830
IAP, 831
IAR, 832
IAS, 833
IAV, 834
ILTVR, 835
IM, 836
IM11, 837
IS, 838
ISJB, 839
ISMR4, 840
ISMR6, 841
ISSI, 842
IVSAV, 843
JB4, 844
JCF10, 845
KPNLT, 846
KVMR, 847
LCM, 848
LDCAA, 849
LDHS, 850
LDP4, 851
LDRN, 852
LDS, 853
LIC, 854
LICAB, 855
LIHS, 856
LIM32, 857
LINSB, 858
LIP4, 859
LIS, 860
LLDS, 861
LNS, 862
LTDB1, 863
LTDB2, 864
LTDB3, 865
LTM, 866
LTPM, 867
LTPP, 868
LTRGE, 869
MA, 870
MBC, 871
MCSM, 872
MFLT, 873
MI, 874
MIVS, 875
MMNC, 876
MNSLE, 877
MOLT, 878
MPMR, 879
MRBE, 880
MRCM, 881
MSCN, 882
MSM, 883
MTV, 884
MWIAA, 885
NDMS4, 886
NIAO, 887
NIAQ, 888
NIAQR, 889
NIDAU, 890
NJB5, 891
NKAO, 892
NLT, 893
NM, 894
NM62, 895
NM64, 896
NM83, 897
NRREF, 898
NSAO, 899
NSAQ, 900
NSAQR, 901
NSC2A, 902
NSC2S, 903
NSC2Z, 904
NSDAT, 905
NSDS, 906
NSE, 907
NSEAI, 908
NSLE, 909
NSLIL, 910
NSNM, 911
NSR, 912
NSS, 913
OLTTR, 914
ONFV, 915
ONTV, 916
OSGMD, 917
OSMC, 918
PCVS, 919
PM, 920
PSHS, 921
PTFP, 922
PTM, 923
PTMEE, 924
RAO, 925
RES, 926
RNM, 927
RNSM, 928
ROD2, 929
ROD4, 930
RREF, 931
RREFN, 932
RRTI, 933
RS, 934
RSAI, 935
RSB, 936
RSC5, 937
RSNS, 938
RSREM, 939
RSSC4, 940
RVMR, 941
S, 942
SAA, 943
SAB, 944
SABMI, 945
SAE, 946
SAN, 947
SAR, 948
SAV, 949
SC, 950
SC3, 951
SCAA, 952
SCAB, 953
SCAD, 954
SDS, 955
SEE, 956
SEEF, 957
SETM, 958
SI, 959
SM2Z7, 960
SM32, 961
SMLT, 962
SMS3, 963
SMS5, 964
SP4, 965
SPIAS, 966
SRR, 967
SS, 968
SS6W, 969
SSC, 970
SSET, 971
SSM22, 972
SSNS, 973
SSP, 974
SSP4, 975
STLT, 976
STNE, 977
SU, 978
SUVOS, 979
SVP4, 980
SYM, 981
TCSD, 982
TD4, 983
TDEE6, 984
TDSSE, 985
TIS, 986
TIVS, 987
TKAP, 988
TLC, 989
TM, 990
TMP, 991
TOV, 992
TREM, 993
TTS, 994
UM3, 995
UPM, 996
US, 997
USR, 998
VA, 999
VESE, 1000
VFS, 1001
VFSAD, 1002
VFSAI, 1003
VFSAL, 1004
VM4, 1005
VRC4, 1006
VRP2, 1007
VSCV, 1008
VSF, 1009
VSIM5, 1010
VSIS, 1011
VSM, 1012
VSP, 1013
VSPUD, 1014
VSS, 1015
ZNDAB, 1016
EXC (subsection, section B), 1017
EXC (subsection, section CB), 1018
EXC (subsection, section CF), 1019
EXC (subsection, section CRS), 1020
EXC (subsection, section D), 1021
EXC (subsection, section DM), 1022
EXC (subsection, section EE), 1023
EXC (subsection, section F), 1024
EXC (subsection, section FS), 1025
EXC (subsection, section HP), 1026
EXC (subsection, section HSE), 1027
EXC (subsection, section ILT), 1028
EXC (subsection, section IVLT), 1029
EXC (subsection, section LC), 1030
EXC (subsection, section LDS), 1031
EXC (subsection, section LI), 1032
EXC (subsection, section LISS), 1033
EXC (subsection, section LT), 1034
EXC (subsection, section MINM), 1035
EXC (subsection, section MISLE), 1036
EXC (subsection, section MM), 1037
EXC (subsection, section MO), 1038
EXC (subsection, section MR), 1039
EXC (subsection, section NM), 1040
EXC (subsection, section O), 1041
EXC (subsection, section PD), 1042
EXC (subsection, section PDM), 1043
EXC (subsection, section PEE), 1044
EXC (subsection, section PSM), 1045
EXC (subsection, section RREF), 1046
EXC (subsection, section S), 1047
EXC (subsection, section SD), 1048
EXC (subsection, section SLT), 1049
EXC (subsection, section SS), 1050
EXC (subsection, section SSLE), 1051
EXC (subsection, section T), 1052
EXC (subsection, section TSS), 1053
EXC (subsection, section VO), 1054
EXC (subsection, section VR), 1055
EXC (subsection, section VS), 1056
EXC (subsection, section WILA), 1057
extended echelon form
submatrices
example SEEF, 1058
extended reduced row-echelon form
properties
theorem PEEF, 1059
F (archetype), 1060
F (definition), 1061
F (section), 1062
F (subsection, section F), 1063
FDV (example), 1064
FF (subsection, section F), 1065
FF8 (example), 1066
Fibonacci sequence
example FSCF, 1067
field
definition F, 1068
figure
CSRST, 1069
DLTA, 1070
DLTM, 1071
DTSLS, 1072
FTMR, 1073
FTMRA, 1074
GLT, 1075
ILT, 1076
MRCLT, 1077
NILT, 1078
FIMP (theorem), 1079
finite field
size 8
example FF8, 1080
four subsets
example FS1, 1081
example FS2, 1082
four subspaces
dimension
theorem DFS, 1083
FRAN (example), 1084
free variables
example CFV, 1085
free variables, number
theorem FVCS, 1086
free, independent variables
example FDV, 1087
FS (section), 1088
FS (subsection, section FS), 1089
FS (subsection, section SD), 1090
FS (theorem), 1091
FS1 (example), 1092
FS2 (example), 1093
FSAG (example), 1094
FSCF (example), 1095
FTMR (figure), 1096
FTMR (theorem), 1097
FTMRA (figure), 1098
FV (subsection, section TSS), 1099
FVCS (theorem), 1100
G (archetype), 1101
G (theorem), 1102
GE4 (example), 1103
GE6 (example), 1104
GEE (subsection, section IS), 1105
GEK (theorem), 1106
generalized eigenspace
as kernel
theorem GEK, 1107
definition GES, 1108
dimension
theorem DGES, 1109
dimension 4 domain
example GE4, 1110
dimension 6 domain
example GE6, 1111
invariant subspace
theorem GESIS, 1112
nilpotent restriction
theorem RGEN, 1113
nilpotent restrictions, dimension 6 domain
example GENR6, 1114
notation, 1115
generalized eigenspace decomposition
theorem GESD, 1116
generalized eigenvector
definition GEV, 1117
GENR6 (example), 1118
GES (definition), 1119
GES (notation), 1120
GESD (subsection, section JCF), 1121
GESD (theorem), 1122
GESIS (theorem), 1123
GEV (definition), 1124
GFDL (appendix), 1125
GLT (figure), 1126
GME (definition), 1127
goldilocks
theorem G, 1128
Gram-Schmidt
column vectors
theorem GSP, 1129
three vectors
example GSTV, 1130
gram-schmidt
mathematica, 1131
GS (technique, section PT), 1132
GSP (subsection, section O), 1133
GSP (theorem), 1134
GSP.MMA (computation, section MMA), 1135
GSTV (example), 1136
GT (subsection, section PD), 1137
H (archetype), 1138
Hadamard Identity
notation, 1139
Hadamard identity
definition HID, 1140
Hadamard Inverse
notation, 1141
Hadamard inverse
definition HI, 1142
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1143
notation, 1144
Hadamard product
commutativity
theorem HPC, 1145
definition HP, 1146
diagonal matrices
theorem DMMP, 1147
distributivity
theorem HPDAA, 1148
example HP, 1149
identity
theorem HPHID, 1150
inverse
theorem HPHI, 1151
scalar matrix multiplication
theorem HPSMM, 1152
hermitian
definition HM, 1153
Hermitian matrix
inner product
theorem HMIP, 1154
HI (definition), 1155
HI (notation), 1156
HID (definition), 1157
HID (notation), 1158
HISAA (example), 1159
HISAD (example), 1160
HM (definition), 1161
HM (subsection, section MM), 1162
HMEM5 (example), 1163
HMIP (theorem), 1164
HMOE (theorem), 1165
HMRE (theorem), 1166
HMVEI (theorem), 1167
homogeneous system
consistent
theorem HSC, 1168
definition HS, 1169
infinitely many solutions
theorem HMVEI, 1170
homogeneous systems
linear independence, 1171
homogenous system
Archetype C
example AHSAC, 1172
HP (definition), 1173
HP (example), 1174
HP (notation), 1175
HP (section), 1176
HPC (theorem), 1177
HPDAA (theorem), 1178
HPDM (example), 1179
HPHI (theorem), 1180
HPHID (theorem), 1181
HPSMM (theorem), 1182
HS (definition), 1183
HSC (theorem), 1184
HSE (section), 1185
HUSAB (example), 1186
I (archetype), 1187
I (technique, section PT), 1188
IAP (example), 1189
IAR (example), 1190
IAS (example), 1191
IAV (example), 1192
ICBM (theorem), 1193
ICLT (theorem), 1194
identities
technique PI, 1195
identity matrix
determinant, 1196
example IM, 1197
notation, 1198
IDLT (definition), 1199
IDV (definition), 1200
IE (definition), 1201
IE (notation), 1202
IFDVS (theorem), 1203
IILT (theorem), 1204
ILT (definition), 1205
ILT (figure), 1206
ILT (section), 1207
ILTB (theorem), 1208
ILTD (subsection, section ILT), 1209
ILTD (theorem), 1210
ILTIS (theorem), 1211
ILTLI (subsection, section ILT), 1212
ILTLI (theorem), 1213
ILTLT (theorem), 1214
ILTVR (example), 1215
IM (definition), 1216
IM (example), 1217
IM (notation), 1218
IM (subsection, section MISLE), 1219
IM11 (example), 1220
IMILT (theorem), 1221
IMP (definition), 1222
IMR (theorem), 1223
inconsistent linear systems
theorem ISRN, 1224
independent, dependent variables
definition IDV, 1225
indesxstring
example SM2Z7, 1226
example SSET, 1227
index
eigenvalue
definition IE, 1228
notation, 1229
indexstring
theorem DRCMA, 1230
theorem OBUTR, 1231
theorem UMCOB, 1232
induction
technique I, 1233
infinite solution set
example ISSI, 1234
infinite solutions,
example IS, 1235
injective
example IAP, 1236
example IAR, 1237
not
example NIAO, 1238
example NIAQ, 1239
example NIAQR, 1240
not, by dimension
example NIDAU, 1241
polynomials to matrices
example IAV, 1242
injective linear transformation
bases
theorem ILTB, 1243
injective linear transformations
dimension
theorem ILTD, 1244
inner product
anti-commutative
theorem IPAC, 1245
example CSIP, 1246
norm
theorem IPN, 1247
notation, 1248
positive
theorem PIP, 1249
scalar multiplication
theorem IPSM, 1250
vector addition
theorem IPVA, 1251
integers
mod
definition IMP, 1252
mod , field
theorem FIMP, 1253
mod 11
example IM11, 1254
interpolating polynomial
theorem IP, 1255
invariant subspace
definition IS, 1256
eigenspace, 1257
eigenspaces
example EIS, 1258
example TIS, 1259
Jordan block
example ISJB, 1260
kernels of powers
theorem KPIS, 1261
inverse
composition of linear transformations
theorem ICLT, 1262
example CMI, 1263
example MI, 1264
notation, 1265
of a matrix, 1266
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1267
invertible linear transformations
composition
theorem CIVLT, 1268
computing
example CIVLT, 1269
IP (definition), 1270
IP (notation), 1271
IP (subsection, section O), 1272
IP (theorem), 1273
IPAC (theorem), 1274
IPN (theorem), 1275
IPSM (theorem), 1276
IPVA (theorem), 1277
IS (definition), 1278
IS (example), 1279
IS (section), 1280
IS (subsection, section IS), 1281
ISJB (example), 1282
ISMR4 (example), 1283
ISMR6 (example), 1284
isomorphic
multiple vector spaces
example MIVS, 1285
vector spaces
example IVSAV, 1286
isomorphic vector spaces
dimension
theorem IVSED, 1287
example TIVS, 1288
ISRN (theorem), 1289
ISSI (example), 1290
ITMT (theorem), 1291
IV (subsection, section IVLT), 1292
IVLT (definition), 1293
IVLT (section), 1294
IVLT (subsection, section IVLT), 1295
IVLT (subsection, section MR), 1296
IVS (definition), 1297
IVSAV (example), 1298
IVSED (theorem), 1299
J (archetype), 1300
JB (definition), 1301
JB (notation), 1302
JB4 (example), 1303
JCF (definition), 1304
JCF (section), 1305
JCF (subsection, section JCF), 1306
JCF10 (example), 1307
JCFLT (theorem), 1308
Jordan block
definition JB, 1309
nilpotent
theorem NJB, 1310
notation, 1311
size 4
example JB4, 1312
Jordan canonical form
definition JCF, 1313
size 10
example JCF10, 1314
K (archetype), 1315
kernel
injective linear transformation
theorem KILT, 1316
isomorphic to null space
theorem KNSI, 1317
linear transformation
example NKAO, 1318
notation, 1319
of a linear transformation
definition KLT, 1320
pre-image, 1321
subspace
theorem KLTS, 1322
trivial
example TKAP, 1323
via matrix representation
example KVMR, 1324
KILT (theorem), 1325
KLT (definition), 1326
KLT (notation), 1327
KLT (subsection, section ILT), 1328
KLTS (theorem), 1329
KNSI (theorem), 1330
KPI (theorem), 1331
KPIS (theorem), 1332
KPLT (theorem), 1333
KPNLT (example), 1334
KPNLT (theorem), 1335
KVMR (example), 1336
L (archetype), 1337
L (technique, section PT), 1338
LA (subsection, section WILA), 1339
LC (definition), 1340
LC (section), 1341
LC (subsection, section LC), 1342
LC (technique, section PT), 1343
LCCV (definition), 1344
LCM (example), 1345
LDCAA (example), 1346
LDHS (example), 1347
LDP4 (example), 1348
LDRN (example), 1349
LDS (example), 1350
LDS (section), 1351
LDSS (subsection, section LDS), 1352
least squares
minimizes residuals
theorem LSMR, 1353
least squares solution
definition LSS, 1354
left null space
as row space, 1355
definition LNS, 1356
example LNS, 1357
notation, 1358
subspace
theorem LNSMS, 1359
lemma
technique LC, 1360
LI (definition), 1361
LI (section), 1362
LI (subsection, section LISS), 1363
LIC (example), 1364
LICAB (example), 1365
LICV (definition), 1366
LIHS (example), 1367
LIM32 (example), 1368
linear combination
system of equations
example ABLC, 1369
definition LC, 1370
definition LCCV, 1371
example TLC, 1372
linear transformation, 1373
matrices
example LCM, 1374
system of equations
example AALC, 1375
linear combinations
solutions to linear systems
theorem SLSLC, 1376
linear dependence
more vectors than size
theorem MVSLD, 1377
linear independence
definition LI, 1378
definition LICV, 1379
homogeneous systems
theorem LIVHS, 1380
injective linear transformation
theorem ILTLI, 1381
matrices
example LIM32, 1382
orthogonal, 1383
r and n
theorem LIVRN, 1384
linear solve
mathematica, 1385
linear system
consistent
theorem RCLS, 1386
matrix representation
definition LSMR, 1387
notation, 1388
linear systems
notation
example MNSLE, 1389
example NSLE, 1390
linear transformation
polynomials to polynomials
example LTPP, 1391
addition
definition LTA, 1392
theorem MLTLT, 1393
theorem SLTLT, 1394
as matrix multiplication
example ALTMM, 1395
basis of range
example BRLT, 1396
checking
example ALT, 1397
composition
definition LTC, 1398
theorem CLTLT, 1399
defined by a matrix
example LTM, 1400
defined on a basis
example LTDB1, 1401
example LTDB2, 1402
example LTDB3, 1403
theorem LTDB, 1404
definition LT, 1405
identity
definition IDLT, 1406
injection
definition ILT, 1407
inverse
theorem ILTLT, 1408
inverse of inverse
theorem IILT, 1409
invertible
definition IVLT, 1410
example AIVLT, 1411
invertible, injective and surjective
theorem ILTIS, 1412
Jordan canonical form
theorem JCFLT, 1413
kernels of powers
theorem KPLT, 1414
linear combination
theorem LTLC, 1415
matrix of, 1416
example MFLT, 1417
example MOLT, 1418
not
example NLT, 1419
not invertible
example ANILT, 1420
notation, 1421
polynomials to matrices
example LTPM, 1422
rank plus nullity
theorem RPNDD, 1423
restriction
definition LTR, 1424
notation, 1425
scalar multiple
example SMLT, 1426
scalar multiplication
definition LTSM, 1427
spanning range
theorem SSRLT, 1428
sum
example STLT, 1429
surjection
definition SLT, 1430
vector space of, 1431
zero vector
theorem LTTZZ, 1432
linear transformation inverse
via matrix representation
example ILTVR, 1433
linear transformation restriction
on generalized eigenspace
example LTRGE, 1434
linear transformations
compositions
example CTLT, 1435
from matrices
theorem MBLT, 1436
linearly dependent
example LDRN, 1437
via homogeneous system
example LDHS, 1438
linearly dependent columns
Archetype A
example LDCAA, 1439
linearly dependent set
example LDS, 1440
linear combinations within
theorem DLDS, 1441
polynomials
example LDP4, 1442
linearly independent
crazy vector space
example LIC, 1443
extending sets
theorem ELIS, 1444
polynomials
example LIP4, 1445
via homogeneous system
example LIHS, 1446
linearly independent columns
Archetype B
example LICAB, 1447
linearly independent set
example LIS, 1448
example LLDS, 1449
LINM (subsection, section LI), 1450
LINSB (example), 1451
LIP4 (example), 1452
LIS (example), 1453
LISS (section), 1454
LISV (subsection, section LI), 1455
LIVHS (theorem), 1456
LIVRN (theorem), 1457
LLDS (example), 1458
LNS (definition), 1459
LNS (example), 1460
LNS (notation), 1461
LNS (subsection, section FS), 1462
LNSMS (theorem), 1463
lower triangular matrix
definition LTM, 1464
LS.MMA (computation, section MMA), 1465
LSMR (definition), 1466
LSMR (notation), 1467
LSMR (theorem), 1468
LSS (definition), 1469
LT (acronyms, section IVLT), 1470
LT (chapter), 1471
LT (definition), 1472
LT (notation), 1473
LT (section), 1474
LT (subsection, section LT), 1475
LTA (definition), 1476
LTC (definition), 1477
LTC (subsection, section LT), 1478
LTDB (theorem), 1479
LTDB1 (example), 1480
LTDB2 (example), 1481
LTDB3 (example), 1482
LTLC (subsection, section LT), 1483
LTLC (theorem), 1484
LTM (definition), 1485
LTM (example), 1486
LTPM (example), 1487
LTPP (example), 1488
LTR (definition), 1489
LTR (notation), 1490
LTRGE (example), 1491
LTSM (definition), 1492
LTTZZ (theorem), 1493
M (acronyms, section FS), 1494
M (archetype), 1495
M (chapter), 1496
M (definition), 1497
M (notation), 1498
MA (definition), 1499
MA (example), 1500
MA (notation), 1501
MACN (Property), 1502
MAF (Property), 1503
MAP (subsection, section SVD), 1504
mathematica
gram-schmidt (computation), 1505
linear solve (computation), 1506
matrix entry (computation), 1507
matrix inverse (computation), 1508
matrix multiplication (computation), 1509
null space (computation), 1510
row reduce (computation), 1511
transpose of a matrix (computation), 1512
vector form of solutions (computation), 1513
vector linear combinations (computation), 1514
mathematical language
technique L, 1515
matrix
addition
definition MA, 1516
notation, 1517
augmented
definition AM, 1518
column space
definition CSM, 1519
complex conjugate
example CCM, 1520
definition M, 1521
equality
definition ME, 1522
notation, 1523
example AM, 1524
identity
definition IM, 1525
inverse
definition MI, 1526
nonsingular
definition NM, 1527
notation, 1528
of a linear transformation
theorem MLTCV, 1529
product
example PTM, 1530
example PTMEE, 1531
product with vector
definition MVP, 1532
rectangular, 1533
row space
definition RSM, 1534
scalar multiplication
definition MSM, 1535
notation, 1536
singular, 1537
square
definition SQM, 1538
submatrices
example SS, 1539
submatrix
definition SM, 1540
symmetric
definition SYM, 1541
transpose
definition TM, 1542
unitary
definition UM, 1543
unitary is invertible
theorem UMI, 1544
zero
definition ZM, 1545
matrix addition
example MA, 1546
matrix components
notation, 1547
matrix entry
mathematica, 1548
ti83, 1549
ti86, 1550
matrix inverse
Archetype B, 1551
computation
theorem CINM, 1552
mathematica, 1553
nonsingular matrix
theorem NI, 1554
of a matrix inverse
theorem MIMI, 1555
one-sided
theorem OSIS, 1556
product
theorem SS, 1557
scalar multiple
theorem MISM, 1558
size 2 matrices
theorem TTMI, 1559
transpose
theorem MIT, 1560
uniqueness
theorem MIU, 1561
matrix multiplication
adjoints
theorem MMAD, 1562
associativity
theorem MMA, 1563
complex conjugation
theorem MMCC, 1564
definition MM, 1565
distributivity
theorem MMDAA, 1566
entry-by-entry
theorem EMP, 1567
identity matrix
theorem MMIM, 1568
inner product
theorem MMIP, 1569
mathematica, 1570
noncommutative
example MMNC, 1571
scalar matrix multiplication
theorem MMSMM, 1572
systems of linear equations
theorem SLEMM, 1573
transposes
theorem MMT, 1574
zero matrix
theorem MMZM, 1575
matrix product
as composition of linear transformations
example MPMR, 1576
matrix representation
basis of eigenvectors
example MRBE, 1577
composition of linear transformations
theorem MRCLT, 1578
definition MR, 1579
invertible
theorem IMR, 1580
multiple of a linear transformation
theorem MRMLT, 1581
notation, 1582
restriction to generalized eigenspace
theorem MRRGE, 1583
sum of linear transformations
theorem MRSLT, 1584
theorem FTMR, 1585
upper triangular
theorem UTMR, 1586
matrix representations
converting with change-of-basis
example MRCM, 1587
example OLTTR, 1588
matrix scalar multiplication
example MSM, 1589
matrix vector space
dimension
theorem DM, 1590
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1591
matrix-vector product
example MTV, 1592
notation, 1593
MBC (example), 1594
MBLT (theorem), 1595
MC (notation), 1596
MCC (subsection, section MO), 1597
MCCN (Property), 1598
MCF (Property), 1599
MCN (definition), 1600
MCN (subsection, section CNO), 1601
MCSM (example), 1602
MCT (theorem), 1603
MD (chapter), 1604
ME (definition), 1605
ME (notation), 1606
ME (subsection, section PEE), 1607
ME (technique, section PT), 1608
ME (theorem), 1609
ME.MMA (computation, section MMA), 1610
ME.TI83 (computation, section TI83), 1611
ME.TI86 (computation, section TI86), 1612
MEASM (subsection, section MO), 1613
MFLT (example), 1614
MI (definition), 1615
MI (example), 1616
MI (notation), 1617
MI.MMA (computation, section MMA), 1618
MICN (Property), 1619
MIF (Property), 1620
MIMI (theorem), 1621
MINM (section), 1622
MISLE (section), 1623
MISM (theorem), 1624
MIT (theorem), 1625
MIU (theorem), 1626
MIVS (example), 1627
MLT (subsection, section LT), 1628
MLTCV (theorem), 1629
MLTLT (theorem), 1630
MM (definition), 1631
MM (section), 1632
MM (subsection, section MM), 1633
MM.MMA (computation, section MMA), 1634
MMA (section), 1635
MMA (theorem), 1636
MMAD (theorem), 1637
MMCC (theorem), 1638
MMDAA (theorem), 1639
MMEE (subsection, section MM), 1640
MMIM (theorem), 1641
MMIP (theorem), 1642
MMNC (example), 1643
MMSMM (theorem), 1644
MMT (theorem), 1645
MMZM (theorem), 1646
MNEM (theorem), 1647
MNSLE (example), 1648
MO (section), 1649
MOLT (example), 1650
more variables than equations
example OSGMD, 1651
theorem CMVEI, 1652
MPMR (example), 1653
MR (definition), 1654
MR (notation), 1655
MR (section), 1656
MRBE (example), 1657
MRCB (theorem), 1658
MRCLT (figure), 1659
MRCLT (theorem), 1660
MRCM (example), 1661
MRMLT (theorem), 1662
MRRGE (theorem), 1663
MRS (subsection, section CB), 1664
MRSLT (theorem), 1665
MSCN (example), 1666
MSM (definition), 1667
MSM (example), 1668
MSM (notation), 1669
MTV (example), 1670
multiplicative associativity
complex numbers
Property MACN, 1671
multiplicative closure
complex numbers
Property MCCN, 1672
field
Property MCF, 1673
multiplicative commuativity
complex numbers
Property CMCN, 1674
multiplicative inverse
complex numbers
Property MICN, 1675
MVNSE (subsection, section RREF), 1676
MVP (definition), 1677
MVP (notation), 1678
MVP (subsection, section MM), 1679
MVSLD (theorem), 1680
MWIAA (example), 1681
N (archetype), 1682
N (subsection, section O), 1683
N (technique, section PT), 1684
NDMS4 (example), 1685
negation of statements
technique N, 1686
NEM (theorem), 1687
NI (theorem), 1688
NIAO (example), 1689
NIAQ (example), 1690
NIAQR (example), 1691
NIDAU (example), 1692
nilpotent
linear transformation
definition NLT, 1693
NILT (figure), 1694
NJB (theorem), 1695
NJB5 (example), 1696
NKAO (example), 1697
NLT (definition), 1698
NLT (example), 1699
NLT (section), 1700
NLT (subsection, section NLT), 1701
NLTFO (subsection, section LT), 1702
NM (definition), 1703
NM (example), 1704
NM (section), 1705
NM (subsection, section NM), 1706
NM (subsection, section OD), 1707
NM62 (example), 1708
NM64 (example), 1709
NM83 (example), 1710
NME1 (theorem), 1711
NME2 (theorem), 1712
NME3 (theorem), 1713
NME4 (theorem), 1714
NME5 (theorem), 1715
NME6 (theorem), 1716
NME7 (theorem), 1717
NME8 (theorem), 1718
NME9 (theorem), 1719
NMI (subsection, section MINM), 1720
NMLIC (theorem), 1721
NMPEM (theorem), 1722
NMRRI (theorem), 1723
NMTNS (theorem), 1724
NMUS (theorem), 1725
NOILT (theorem), 1726
NOLT (definition), 1727
NOLT (notation), 1728
NOM (definition), 1729
NOM (notation), 1730
nonsingular
columns as basis
theorem CNMB, 1731
nonsingular matrices
linearly independent columns
theorem NMLIC, 1732
nonsingular matrix
Archetype B
example NM, 1733
column space, 1734
elemntary matrices
theorem NMPEM, 1735
equivalences
theorem NME1, 1736
theorem NME2, 1737
theorem NME3, 1738
theorem NME4, 1739
theorem NME5, 1740
theorem NME6, 1741
theorem NME7, 1742
theorem NME8, 1743
theorem NME9, 1744
matrix inverse, 1745
null space
example NSNM, 1746
nullity, 1747
product of nonsingular matrices
theorem NPNT, 1748
rank
theorem RNNM, 1749
row-reduced
theorem NMRRI, 1750
trivial null space
theorem NMTNS, 1751
unique solutions
theorem NMUS, 1752
nonsingular matrix, row-reduced
example NSR, 1753
norm
example CNSV, 1754
inner product, 1755
notation, 1756
normal matrix
definition NRML, 1757
example ANM, 1758
orthonormal basis, 1759
notation
A, 1760
AM, 1761
C, 1762
CCCV, 1763
CCM, 1764
CCN, 1765
CNA, 1766
CNE, 1767
CNM, 1768
CSM, 1769
CV, 1770
CVA, 1771
CVC, 1772
CVE, 1773
CVSM, 1774
D, 1775
DM, 1776
DS, 1777
ELEM, 1778
ES, 1779
GES, 1780
HI, 1781
HID, 1782
HP, 1783
IE, 1784
IM, 1785
IP, 1786
JB, 1787
KLT, 1788
LNS, 1789
LSMR, 1790
LT, 1791
LTR, 1792
M, 1793
MA, 1794
MC, 1795
ME, 1796
MI, 1797
MR, 1798
MSM, 1799
MVP, 1800
NOLT, 1801
NOM, 1802
NSM, 1803
NV, 1804
RLT, 1805
RO, 1806
ROLT, 1807
ROM, 1808
RREFA, 1809
RSM, 1810
SC, 1811
SE, 1812
SETM, 1813
SI, 1814
SM, 1815
SRM, 1816
SSET, 1817
SSV, 1818
SU, 1819
SUV, 1820
T, 1821
TM, 1822
VR, 1823
VSCV, 1824
VSM, 1825
ZCV, 1826
ZM, 1827
notation for a linear system
example NSE, 1828
NPNT (theorem), 1829
NRFO (subsection, section MR), 1830
NRML (definition), 1831
NRREF (example), 1832
NS.MMA (computation, section MMA), 1833
NSAO (example), 1834
NSAQ (example), 1835
NSAQR (example), 1836
NSC2A (example), 1837
NSC2S (example), 1838
NSC2Z (example), 1839
NSDAT (example), 1840
NSDS (example), 1841
NSE (example), 1842
NSEAI (example), 1843
NSLE (example), 1844
NSLIL (example), 1845
NSM (definition), 1846
NSM (notation), 1847
NSM (subsection, section HSE), 1848
NSMS (theorem), 1849
NSNM (example), 1850
NSNM (subsection, section NM), 1851
NSR (example), 1852
NSS (example), 1853
NSSLI (subsection, section LI), 1854
Null space
as a span
example NSDS, 1855
null space
Archetype I
example NSEAI, 1856
basis
theorem BNS, 1857
computation
example CNS1, 1858
example CNS2, 1859
isomorphic to kernel, 1860
linearly independent basis
example LINSB, 1861
mathematica, 1862
matrix
definition NSM, 1863
nonsingular matrix, 1864
notation, 1865
singular matrix, 1866
spanning set
example SSNS, 1867
theorem SSNS, 1868
subspace
theorem NSMS, 1869
null space span, linearly independent
Archetype L
example NSLIL, 1870
nullity
computing, 1871
injective linear transformation
theorem NOILT, 1872
linear transformation
definition NOLT, 1873
matrix, 1874
definition NOM, 1875
notation, 1876, 1877
square matrix, 1878
NV (definition), 1879
NV (notation), 1880
NVM (theorem), 1881
O (archetype), 1882
O (Property), 1883
O (section), 1884
OBC (subsection, section B), 1885
OBNM (theorem), 1886
OBUTR (theorem), 1887
OC (Property), 1888
OCN (Property), 1889
OD (section), 1890
OD (subsection, section OD), 1891
OD (theorem), 1892
OF (Property), 1893
OLTTR (example), 1894
OM (Property), 1895
one
column vectors
Property OC, 1896
complex numbers
Property OCN, 1897
field
Property OF, 1898
matrices
Property OM, 1899
vectors
Property O, 1900
ONFV (example), 1901
ONS (definition), 1902
ONTV (example), 1903
orthogonal
linear independence
theorem OSLI, 1904
set
example AOS, 1905
set of vectors
definition OSV, 1906
vector pairs
definition OV, 1907
orthogonal vectors
example TOV, 1908
orthonormal
definition ONS, 1909
matrix columns
example OSMC, 1910
orthonormal basis
normal matrix
theorem OBNM, 1911
orthonormal diagonalization
theorem OD, 1912
orthonormal set
four vectors
example ONFV, 1913
three vectors
example ONTV, 1914
OSGMD (example), 1915
OSIS (theorem), 1916
OSLI (theorem), 1917
OSMC (example), 1918
OSV (definition), 1919
OV (definition), 1920
OV (subsection, section O), 1921
P (appendix), 1922
P (archetype), 1923
P (technique, section PT), 1924
particular solutions
example PSHS, 1925
PCNA (theorem), 1926
PCVS (example), 1927
PD (section), 1928
PDM (section), 1929
PDM (theorem), 1930
PEE (section), 1931
PEEF (theorem), 1932
PI (definition), 1933
PI (subsection, section LT), 1934
PI (technique, section PT), 1935
PIP (theorem), 1936
PM (example), 1937
PM (subsection, section EE), 1938
PMI (subsection, section MISLE), 1939
PMM (subsection, section MM), 1940
PMR (subsection, section MR), 1941
PNLT (subsection, section NLT), 1942
POD (section), 1943
polar decomposition
theorem PDM, 1944
polynomial
of a matrix
example PM, 1945
polynomial vector space
dimension
theorem DP, 1946
positive semi-definite
creating
theorem CPSM, 1947
positive semi-definite matrix
definition PSM, 1948
eigenvalues
theorem EPSM, 1949
practice
technique P, 1950
pre-image
definition PI, 1951
kernel
theorem KPI, 1952
pre-images
example SPIAS, 1953
principal axis theorem, 1954
product of triangular matrices
theorem PTMT, 1955
Property
AA, 1956
AAC, 1957
AACN, 1958
AAF, 1959
AAM, 1960
AC, 1961
ACC, 1962
ACCN, 1963
ACF, 1964
ACM, 1965
AI, 1966
AIC, 1967
AICN, 1968
AIF, 1969
AIM, 1970
C, 1971
CACN, 1972
CAF, 1973
CC, 1974
CM, 1975
CMCN, 1976
CMF, 1977
DCN, 1978
DF, 1979
DMAM, 1980
DSA, 1981
DSAC, 1982
DSAM, 1983
DVA, 1984
DVAC, 1985
MACN, 1986
MAF, 1987
MCCN, 1988
MCF, 1989
MICN, 1990
MIF, 1991
O, 1992
OC, 1993
OCN, 1994
OF, 1995
OM, 1996
SC, 1997
SCC, 1998
SCM, 1999
SMA, 2000
SMAC, 2001
SMAM, 2002
Z, 2003
ZC, 2004
ZCN, 2005
ZF, 2006
ZM, 2007
PSHS (example), 2008
PSHS (subsection, section LC), 2009
PSM (definition), 2010
PSM (section), 2011
PSM (subsection, section PSM), 2012
PSM (subsection, section SD), 2013
PSMSR (theorem), 2014
PSPHS (theorem), 2015
PSS (subsection, section SSLE), 2016
PSSD (theorem), 2017
PSSLS (theorem), 2018
PT (section), 2019
PTFP (example), 2020
PTM (example), 2021
PTMEE (example), 2022
PTMT (theorem), 2023
Q (archetype), 2024
R (acronyms, section JCF), 2025
R (archetype), 2026
R (chapter), 2027
range
full
example FRAN, 2028
isomorphic to column space
theorem RCSI, 2029
linear transformation
example RAO, 2030
notation, 2031
of a linear transformation
definition RLT, 2032
pre-image
theorem RPI, 2033
subspace
theorem RLTS, 2034
surjective linear transformation
theorem RSLT, 2035
via matrix representation
example RVMR, 2036
rank
computing
theorem CRN, 2037
linear transformation
definition ROLT, 2038
matrix
definition ROM, 2039
example RNM, 2040
notation, 2041, 2042
of transpose
example RRTI, 2043
square matrix
example RNSM, 2044
surjective linear transformation
theorem ROSLT, 2045
transpose
theorem RMRT, 2046
rank one decomposition
size 2
example ROD2, 2047
size 4
example ROD4, 2048
theorem ROD, 2049
rank+nullity
theorem RPNC, 2050
RAO (example), 2051
RCLS (theorem), 2052
RCSI (theorem), 2053
RD (subsection, section VS), 2054
RDS (theorem), 2055
READ (subsection, section B), 2056
READ (subsection, section CB), 2057
READ (subsection, section CRS), 2058
READ (subsection, section D), 2059
READ (subsection, section DM), 2060
READ (subsection, section EE), 2061
READ (subsection, section FS), 2062
READ (subsection, section HSE), 2063
READ (subsection, section ILT), 2064
READ (subsection, section IVLT), 2065
READ (subsection, section LC), 2066
READ (subsection, section LDS), 2067
READ (subsection, section LI), 2068
READ (subsection, section LISS), 2069
READ (subsection, section LT), 2070
READ (subsection, section MINM), 2071
READ (subsection, section MISLE), 2072
READ (subsection, section MM), 2073
READ (subsection, section MO), 2074
READ (subsection, section MR), 2075
READ (subsection, section NM), 2076
READ (subsection, section O), 2077
READ (subsection, section PD), 2078
READ (subsection, section PDM), 2079
READ (subsection, section PEE), 2080
READ (subsection, section RREF), 2081
READ (subsection, section S), 2082
READ (subsection, section SD), 2083
READ (subsection, section SLT), 2084
READ (subsection, section SS), 2085
READ (subsection, section SSLE), 2086
READ (subsection, section TSS), 2087
READ (subsection, section VO), 2088
READ (subsection, section VR), 2089
READ (subsection, section VS), 2090
READ (subsection, section WILA), 2091
reduced row-echelon form
analysis
notation, 2092
definition RREF, 2093
example NRREF, 2094
example RREF, 2095
extended
definition EEF, 2096
notation
example RREFN, 2097
unique
theorem RREFU, 2098
reducing a span
example RSC5, 2099
relation of linear dependence
definition RLD, 2100
definition RLDCV, 2101
REM (definition), 2102
REMEF (theorem), 2103
REMES (theorem), 2104
REMRS (theorem), 2105
RES (example), 2106
RGEN (theorem), 2107
RLD (definition), 2108
RLDCV (definition), 2109
RLT (definition), 2110
RLT (notation), 2111
RLT (subsection, section IS), 2112
RLT (subsection, section SLT), 2113
RLTS (theorem), 2114
RMRT (theorem), 2115
RNLT (subsection, section IVLT), 2116
RNM (example), 2117
RNM (subsection, section D), 2118
RNNM (subsection, section D), 2119
RNNM (theorem), 2120
RNSM (example), 2121
RO (definition), 2122
RO (notation), 2123
RO (subsection, section RREF), 2124
ROD (section), 2125
ROD (theorem), 2126
ROD2 (example), 2127
ROD4 (example), 2128
ROLT (definition), 2129
ROLT (notation), 2130
ROM (definition), 2131
ROM (notation), 2132
ROSLT (theorem), 2133
row operations
definition RO, 2134
elementary matrices, 2135, 2136
notation, 2137
row reduce
mathematica, 2138
ti83, 2139
ti86, 2140
row space
Archetype I
example RSAI, 2141
as column space, 2142
basis
example RSB, 2143
theorem BRS, 2144
matrix, 2145
notation, 2146
row-equivalent matrices
theorem REMRS, 2147
subspace
theorem RSMS, 2148
row-equivalent matrices
definition REM, 2149
example TREM, 2150
row space, 2151
row spaces
example RSREM, 2152
theorem REMES, 2153
row-reduce
the verb
definition RR, 2154
row-reduced matrices
theorem REMEF, 2155
RPI (theorem), 2156
RPNC (theorem), 2157
RPNDD (theorem), 2158
RR (definition), 2159
RR.MMA (computation, section MMA), 2160
RR.TI83 (computation, section TI83), 2161
RR.TI86 (computation, section TI86), 2162
RREF (definition), 2163
RREF (example), 2164
RREF (section), 2165
RREF (subsection, section RREF), 2166
RREFA (notation), 2167
RREFN (example), 2168
RREFU (theorem), 2169
RRTI (example), 2170
RS (example), 2171
RSAI (example), 2172
RSB (example), 2173
RSC5 (example), 2174
RSLT (theorem), 2175
RSM (definition), 2176
RSM (notation), 2177
RSM (subsection, section CRS), 2178
RSMS (theorem), 2179
RSNS (example), 2180
RSREM (example), 2181
RSSC4 (example), 2182
RT (subsection, section PD), 2183
RVMR (example), 2184
S (archetype), 2185
S (definition), 2186
S (example), 2187
S (section), 2188
SAA (example), 2189
SAB (example), 2190
SABMI (example), 2191
SAE (example), 2192
SAN (example), 2193
SAR (example), 2194
SAS (section), 2195
SAV (example), 2196
SC (definition), 2197
SC (example), 2198
SC (notation), 2199
SC (Property), 2200
SC (subsection, section S), 2201
SC (subsection, section SET), 2202
SC3 (example), 2203
SCAA (example), 2204
SCAB (example), 2205
SCAD (example), 2206
scalar closure
column vectors
Property SCC, 2207
matrices
Property SCM, 2208
vectors
Property SC, 2209
scalar multiple
matrix inverse, 2210
scalar multiplication
zero scalar
theorem ZSSM, 2211
zero vector
theorem ZVSM, 2212
zero vector result
theorem SMEZV, 2213
scalar multiplication associativity
column vectors
Property SMAC, 2214
matrices
Property SMAM, 2215
vectors
Property SMA, 2216
SCB (theorem), 2217
SCC (Property), 2218
SCM (Property), 2219
SD (section), 2220
SDS (example), 2221
SE (definition), 2222
SE (notation), 2223
secret sharing
6 ways
example SS6W, 2224
SEE (example), 2225
SEEF (example), 2226
SER (theorem), 2227
set
cardinality
definition C, 2228
example CS, 2229
notation, 2230
complement
definition SC, 2231
example SC, 2232
notation, 2233
definition SET, 2234
empty
definition ES, 2235
equality
definition SE, 2236
notation, 2237
intersection
definition SI, 2238
example SI, 2239
notation, 2240
membership
example SETM, 2241
notation, 2242
size, 2243
subset, 2244
union
definition SU, 2245
example SU, 2246
notation, 2247
SET (definition), 2248
SET (section), 2249
SETM (example), 2250
SETM (notation), 2251
shoes, 2252
SHS (subsection, section HSE), 2253
SI (definition), 2254
SI (example), 2255
SI (notation), 2256
SI (subsection, section IVLT), 2257
SIM (definition), 2258
similar matrices
equal eigenvalues
example EENS, 2259
eual eigenvalues
theorem SMEE, 2260
example SMS3, 2261
example SMS5, 2262
similarity
definition SIM, 2263
equivalence relation
theorem SER, 2264
singular matrix
Archetype A
example S, 2265
null space
example NSS, 2266
singular matrix, row-reduced
example SRR, 2267
singular value decomposition
theorem SVD, 2268
singular values
definition SV, 2269
SLE (acronyms, section NM), 2270
SLE (chapter), 2271
SLE (definition), 2272
SLE (subsection, section SSLE), 2273
SLELT (subsection, section IVLT), 2274
SLEMM (theorem), 2275
SLSLC (theorem), 2276
SLT (definition), 2277
SLT (section), 2278
SLTB (theorem), 2279
SLTD (subsection, section SLT), 2280
SLTD (theorem), 2281
SLTLT (theorem), 2282
SM (definition), 2283
SM (notation), 2284
SM (subsection, section SD), 2285
SM2Z7 (example), 2286
SM32 (example), 2287
SMA (Property), 2288
SMAC (Property), 2289
SMAM (Property), 2290
SMEE (theorem), 2291
SMEZV (theorem), 2292
SMLT (example), 2293
SMS (theorem), 2294
SMS3 (example), 2295
SMS5 (example), 2296
SMZD (theorem), 2297
SMZE (theorem), 2298
SNCM (theorem), 2299
SO (subsection, section SET), 2300
socks, 2301
SOL (subsection, section B), 2302
SOL (subsection, section CB), 2303
SOL (subsection, section CRS), 2304
SOL (subsection, section D), 2305
SOL (subsection, section DM), 2306
SOL (subsection, section EE), 2307
SOL (subsection, section F), 2308
SOL (subsection, section FS), 2309
SOL (subsection, section HSE), 2310
SOL (subsection, section ILT), 2311
SOL (subsection, section IVLT), 2312
SOL (subsection, section LC), 2313
SOL (subsection, section LDS), 2314
SOL (subsection, section LI), 2315
SOL (subsection, section LISS), 2316
SOL (subsection, section LT), 2317
SOL (subsection, section MINM), 2318
SOL (subsection, section MISLE), 2319
SOL (subsection, section MM), 2320
SOL (subsection, section MO), 2321
SOL (subsection, section MR), 2322
SOL (subsection, section NM), 2323
SOL (subsection, section O), 2324
SOL (subsection, section PD), 2325
SOL (subsection, section PDM), 2326
SOL (subsection, section PEE), 2327
SOL (subsection, section RREF), 2328
SOL (subsection, section S), 2329
SOL (subsection, section SD), 2330
SOL (subsection, section SLT), 2331
SOL (subsection, section SS), 2332
SOL (subsection, section SSLE), 2333
SOL (subsection, section T), 2334
SOL (subsection, section TSS), 2335
SOL (subsection, section VO), 2336
SOL (subsection, section VR), 2337
SOL (subsection, section VS), 2338
SOL (subsection, section WILA), 2339
solution set
Archetype A
example SAA, 2340
archetype E
example SAE, 2341
theorem PSPHS, 2342
solution sets
possibilities
theorem PSSLS, 2343
solution vector
definition SOLV, 2344
SOLV (definition), 2345
solving homogeneous system
Archetype A
example HISAA, 2346
Archetype B
example HUSAB, 2347
Archetype D
example HISAD, 2348
solving nonlinear equations
example STNE, 2349
SP4 (example), 2350
span
basic
example ABS, 2351
basis
theorem BS, 2352
definition SS, 2353
definition SSCV, 2354
improved
example IAS, 2355
notation, 2356
reducing
example RSSC4, 2357
reduction
example RS, 2358
removing vectors
example COV, 2359
reworking elements
example RES, 2360
set of polynomials
example SSP, 2361
subspace
theorem SSS, 2362
span of columns
Archetype A
example SCAA, 2363
Archetype B
example SCAB, 2364
Archetype D
example SCAD, 2365
spanning set
crazy vector space
example SSC, 2366
definition TSVS, 2367
matrices
example SSM22, 2368
more vectors
theorem SSLD, 2369
polynomials
example SSP4, 2370
SPIAS (example), 2371
SQM (definition), 2372
square root
eigenvalues, eigenspaces
theorem EESR, 2373
matrix
definition SRM, 2374
notation, 2375
positive semi-definite matrix
theorem PSMSR, 2376
unique
theorem USR, 2377
SR (section), 2378
SRM (definition), 2379
SRM (notation), 2380
SRM (subsection, section SR), 2381
SRR (example), 2382
SS (definition), 2383
SS (example), 2384
SS (section), 2385
SS (subsection, section LISS), 2386
SS (theorem), 2387
SS6W (example), 2388
SSC (example), 2389
SSCV (definition), 2390
SSET (definition), 2391
SSET (example), 2392
SSET (notation), 2393
SSLD (theorem), 2394
SSLE (section), 2395
SSM22 (example), 2396
SSNS (example), 2397
SSNS (subsection, section SS), 2398
SSNS (theorem), 2399
SSP (example), 2400
SSP4 (example), 2401
SSRLT (theorem), 2402
SSS (theorem), 2403
SSSLT (subsection, section SLT), 2404
SSV (notation), 2405
SSV (subsection, section SS), 2406
standard unit vector
notation, 2407
starting proofs
technique GS, 2408
STLT (example), 2409
STNE (example), 2410
SU (definition), 2411
SU (example), 2412
SU (notation), 2413
submatrix
notation, 2414
subset
definition SSET, 2415
notation, 2416
subspace
as null space
example RSNS, 2417
characterized
example ASC, 2418
definition S, 2419
in
example SP4, 2420
not, additive closure
example NSC2A, 2421
not, scalar closure
example NSC2S, 2422
not, zero vector
example NSC2Z, 2423
testing
theorem TSS, 2424
trivial
definition TS, 2425
verification
example SC3, 2426
example SM32, 2427
subspaces
equal dimension
theorem EDYES, 2428
surjective
Archetype N
example SAN, 2429
example SAR, 2430
not
example NSAQ, 2431
example NSAQR, 2432
not, Archetype O
example NSAO, 2433
not, by dimension
example NSDAT, 2434
polynomials to matrices
example SAV, 2435
surjective linear transformation
bases
theorem SLTB, 2436
surjective linear transformations
dimension
theorem SLTD, 2437
SUV (definition), 2438
SUV (notation), 2439
SUVB (theorem), 2440
SUVOS (example), 2441
SV (definition), 2442
SVD (section), 2443
SVD (subsection, section SVD), 2444
SVD (theorem), 2445
SVP4 (example), 2446
SYM (definition), 2447
SYM (example), 2448
symmetric matrices
theorem SMS, 2449
symmetric matrix
example SYM, 2450
system of equations
vector equality
example VESE, 2451
system of linear equations
definition SLE, 2452
T (archetype), 2453
T (definition), 2454
T (notation), 2455
T (part), 2456
T (section), 2457
T (technique, section PT), 2458
TCSD (example), 2459
TD (section), 2460
TD (subsection, section TD), 2461
TD (theorem), 2462
TD4 (example), 2463
TDEE (theorem), 2464
TDEE6 (example), 2465
TDSSE (example), 2466
TDSSE (subsection, section TD), 2467
technique
C, 2468
CD, 2469
CP, 2470
CV, 2471
D, 2472
DC, 2473
E, 2474
GS, 2475
I, 2476
L, 2477
LC, 2478
ME, 2479
N, 2480
P, 2481
PI, 2482
T, 2483
U, 2484
theorem
AA, 2485
AIP, 2486
AISM, 2487
AIU, 2488
AMA, 2489
AMSM, 2490
BCS, 2491
BIS, 2492
BNS, 2493
BRS, 2494
BS, 2495
CB, 2496
CCM, 2497
CCRA, 2498
CCRM, 2499
CCT, 2500
CFDVS, 2501
CFNLT, 2502
CHT, 2503
CILTI, 2504
CINM, 2505
CIVLT, 2506
CLI, 2507
CLTLT, 2508
CMVEI, 2509
CNMB, 2510
COB, 2511
CPSM, 2512
CRMA, 2513
CRMSM, 2514
CRN, 2515
CRSM, 2516
CRVA, 2517
CSCS, 2518
CSLTS, 2519
CSMS, 2520
CSNM, 2521
CSRN, 2522
CSRST, 2523
CSS, 2524
CUMOS, 2525
DC, 2526
DCM, 2527
DCP, 2528
DEC, 2529
DED, 2530
DEM, 2531
DEMMM, 2532
DER, 2533
DERC, 2534
DFS, 2535
DGES, 2536
DIM, 2537
DLDS, 2538
DM, 2539
DMFE, 2540
DMHP, 2541
DMMP, 2542
DMST, 2543
DNLT, 2544
DP, 2545
DRCM, 2546
DRCMA, 2547
DRCS, 2548
DRMM, 2549
DSD, 2550
DSFB, 2551
DSFOS, 2552
DSLI, 2553
DSZI, 2554
DSZV, 2555
DT, 2556
DVM, 2557
DZRC, 2558
EDELI, 2559
EDYES, 2560
EEMAP, 2561
EER, 2562
EESR, 2563
EIM, 2564
EIS, 2565
ELIS, 2566
EMDRO, 2567
EMHE, 2568
EMMVP, 2569
EMN, 2570
EMNS, 2571
EMP, 2572
EMRCP, 2573
EMS, 2574
ENLT, 2575
EOMP, 2576
EOPSS, 2577
EPM, 2578
EPSM, 2579
ERMCP, 2580
ESMM, 2581
ETM, 2582
FIMP, 2583
FS, 2584
FTMR, 2585
FVCS, 2586
G, 2587
GEK, 2588
GESD, 2589
GESIS, 2590
GSP, 2591
HMIP, 2592
HMOE, 2593
HMRE, 2594
HMVEI, 2595
HPC, 2596
HPDAA, 2597
HPHI, 2598
HPHID, 2599
HPSMM, 2600
HSC, 2601
ICBM, 2602
ICLT, 2603
IFDVS, 2604
IILT, 2605
ILTB, 2606
ILTD, 2607
ILTIS, 2608
ILTLI, 2609
ILTLT, 2610
IMILT, 2611
IMR, 2612
IP, 2613
IPAC, 2614
IPN, 2615
IPSM, 2616
IPVA, 2617
ISRN, 2618
ITMT, 2619
IVSED, 2620
JCFLT, 2621
KILT, 2622
KLTS, 2623
KNSI, 2624
KPI, 2625
KPIS, 2626
KPLT, 2627
KPNLT, 2628
LIVHS, 2629
LIVRN, 2630
LNSMS, 2631
LSMR, 2632
LTDB, 2633
LTLC, 2634
LTTZZ, 2635
MBLT, 2636
MCT, 2637
ME, 2638
MIMI, 2639
MISM, 2640
MIT, 2641
MIU, 2642
MLTCV, 2643
MLTLT, 2644
MMA, 2645
MMAD, 2646
MMCC, 2647
MMDAA, 2648
MMIM, 2649
MMIP, 2650
MMSMM, 2651
MMT, 2652
MMZM, 2653
MNEM, 2654
MRCB, 2655
MRCLT, 2656
MRMLT, 2657
MRRGE, 2658
MRSLT, 2659
MVSLD, 2660
NEM, 2661
NI, 2662
NJB, 2663
NME1, 2664
NME2, 2665
NME3, 2666
NME4, 2667
NME5, 2668
NME6, 2669
NME7, 2670
NME8, 2671
NME9, 2672
NMLIC, 2673
NMPEM, 2674
NMRRI, 2675
NMTNS, 2676
NMUS, 2677
NOILT, 2678
NPNT, 2679
NSMS, 2680
NVM, 2681
OBNM, 2682
OBUTR, 2683
OD, 2684
OSIS, 2685
OSLI, 2686
PCNA, 2687
PDM, 2688
PEEF, 2689
PIP, 2690
PSMSR, 2691
PSPHS, 2692
PSSD, 2693
PSSLS, 2694
PTMT, 2695
RCLS, 2696
RCSI, 2697
RDS, 2698
REMEF, 2699
REMES, 2700
REMRS, 2701
RGEN, 2702
RLTS, 2703
RMRT, 2704
RNNM, 2705
ROD, 2706
ROSLT, 2707
RPI, 2708
RPNC, 2709
RPNDD, 2710
RREFU, 2711
RSLT, 2712
RSMS, 2713
SCB, 2714
SER, 2715
SLEMM, 2716
SLSLC, 2717
SLTB, 2718
SLTD, 2719
SLTLT, 2720
SMEE, 2721
SMEZV, 2722
SMS, 2723
SMZD, 2724
SMZE, 2725
SNCM, 2726
SS, 2727
SSLD, 2728
SSNS, 2729
SSRLT, 2730
SSS, 2731
SUVB, 2732
SVD, 2733
TD, 2734
TDEE, 2735
technique T, 2736
TIST, 2737
TL, 2738
TMA, 2739
TMSM, 2740
TSE, 2741
TSRM, 2742
TSS, 2743
TT, 2744
TTMI, 2745
UMCOB, 2746
UMI, 2747
UMPIP, 2748
USR, 2749
UTMR, 2750
VFSLS, 2751
VRI, 2752
VRILT, 2753
VRLT, 2754
VRRB, 2755
VRS, 2756
VSLT, 2757
VSPCV, 2758
VSPM, 2759
ZSSM, 2760
ZVSM, 2761
ZVU, 2762
ti83
matrix entry (computation), 2763
row reduce (computation), 2764
vector linear combinations (computation), 2765
TI83 (section), 2766
ti86
matrix entry (computation), 2767
row reduce (computation), 2768
transpose of a matrix (computation), 2769
vector linear combinations (computation), 2770
TI86 (section), 2771
TIS (example), 2772
TIST (theorem), 2773
TIVS (example), 2774
TKAP (example), 2775
TL (theorem), 2776
TLC (example), 2777
TM (definition), 2778
TM (example), 2779
TM (notation), 2780
TM (subsection, section OD), 2781
TM.MMA (computation, section MMA), 2782
TM.TI86 (computation, section TI86), 2783
TMA (theorem), 2784
TMP (example), 2785
TMSM (theorem), 2786
TOV (example), 2787
trace
definition T, 2788
linearity
theorem TL, 2789
matrix multiplication
theorem TSRM, 2790
notation, 2791
similarity
theorem TIST, 2792
sum of eigenvalues
theorem TSE, 2793
trail mix
example TMP, 2794
transpose
matrix scalar multiplication
theorem TMSM, 2795
example TM, 2796
matrix addition
theorem TMA, 2797
matrix inverse, 2798, 2799
notation, 2800
scalar multiplication, 2801
transpose of a matrix
mathematica, 2802
ti86, 2803
transpose of a transpose
theorem TT, 2804
TREM (example), 2805
triangular decomposition
entry by entry, size 6
example TDEE6, 2806
entry by entry
theorem TDEE, 2807
size 4
example TD4, 2808
solving systems of equations
example TDSSE, 2809
theorem TD, 2810
triangular matrix
inverse
theorem ITMT, 2811
trivial solution
system of equations
definition TSHSE, 2812
TS (definition), 2813
TS (subsection, section S), 2814
TSE (theorem), 2815
TSHSE (definition), 2816
TSM (subsection, section MO), 2817
TSRM (theorem), 2818
TSS (section), 2819
TSS (subsection, section S), 2820
TSS (theorem), 2821
TSVS (definition), 2822
TT (theorem), 2823
TTMI (theorem), 2824
TTS (example), 2825
typical systems,
example TTS, 2826
U (archetype), 2827
U (technique, section PT), 2828
UM (definition), 2829
UM (subsection, section MINM), 2830
UM3 (example), 2831
UMCOB (theorem), 2832
UMI (theorem), 2833
UMPIP (theorem), 2834
unique solution,
example US, 2835
example USR, 2836
uniqueness
technique U, 2837
unit vectors
basis
theorem SUVB, 2838
definition SUV, 2839
orthogonal
example SUVOS, 2840
unitary
permutation matrix
example UPM, 2841
size 3
example UM3, 2842
unitary matrices
columns
theorem CUMOS, 2843
unitary matrix
inner product
theorem UMPIP, 2844
UPM (example), 2845
upper triangular matrix
definition UTM, 2846
US (example), 2847
USR (example), 2848
USR (theorem), 2849
UTM (definition), 2850
UTMR (subsection, section OD), 2851
UTMR (theorem), 2852
V (acronyms, section O), 2853
V (archetype), 2854
V (chapter), 2855
VA (example), 2856
Vandermonde matrix
definition VM, 2857
vandermonde matrix
determinant
theorem DVM, 2858
nonsingular
theorem NVM, 2859
size 4
example VM4, 2860
VEASM (subsection, section VO), 2861
vector
addition
definition CVA, 2862
column
definition CV, 2863
equality
definition CVE, 2864
notation, 2865
inner product
definition IP, 2866
norm
definition NV, 2867
notation, 2868
of constants
definition VOC, 2869
product with matrix, 2870, 2871
scalar multiplication
definition CVSM, 2872
vector addition
example VA, 2873
vector component
notation, 2874
vector form of solutions
Archetype D
example VFSAD, 2875
Archetype I
example VFSAI, 2876
Archetype L
example VFSAL, 2877
example VFS, 2878
mathematica, 2879
theorem VFSLS, 2880
vector linear combinations
mathematica, 2881
ti83, 2882
ti86, 2883
vector representation
example AVR, 2884
example VRC4, 2885
injective
theorem VRI, 2886
invertible
theorem VRILT, 2887
linear transformation
definition VR, 2888
notation, 2889
theorem VRLT, 2890
surjective
theorem VRS, 2891
theorem VRRB, 2892
vector representations
polynomials
example VRP2, 2893
vector scalar multiplication
example CVSM, 2894
vector space
characterization
theorem CFDVS, 2895
column vectors
definition VSCV, 2896
definition VS, 2897
infinite dimension
example VSPUD, 2898
linear transformations
theorem VSLT, 2899
over integers mod 5
example VSIM5, 2900
vector space of column vectors
notation, 2901
vector space of functions
example VSF, 2902
vector space of infinite sequences
example VSIS, 2903
vector space of matrices
definition VSM, 2904
example VSM, 2905
notation, 2906
vector space of polynomials
example VSP, 2907
vector space properties
column vectors
theorem VSPCV, 2908
matrices
theorem VSPM, 2909
vector space, crazy
example CVS, 2910
vector space, singleton
example VSS, 2911
vector spaces
isomorphic
definition IVS, 2912
theorem IFDVS, 2913
VESE (example), 2914
VFS (example), 2915
VFSAD (example), 2916
VFSAI (example), 2917
VFSAL (example), 2918
VFSLS (theorem), 2919
VFSS (subsection, section LC), 2920
VFSS.MMA (computation, section MMA), 2921
VLC.MMA (computation, section MMA), 2922
VLC.TI83 (computation, section TI83), 2923
VLC.TI86 (computation, section TI86), 2924
VM (definition), 2925
VM (section), 2926
VM4 (example), 2927
VO (section), 2928
VOC (definition), 2929
VR (definition), 2930
VR (notation), 2931
VR (section), 2932
VR (subsection, section LISS), 2933
VRC4 (example), 2934
VRI (theorem), 2935
VRILT (theorem), 2936
VRLT (theorem), 2937
VRP2 (example), 2938
VRRB (theorem), 2939
VRS (theorem), 2940
VS (acronyms, section PD), 2941
VS (chapter), 2942
VS (definition), 2943
VS (section), 2944
VS (subsection, section VS), 2945
VSCV (definition), 2946
VSCV (example), 2947
VSCV (notation), 2948
VSF (example), 2949
VSIM5 (example), 2950
VSIS (example), 2951
VSLT (theorem), 2952
VSM (definition), 2953
VSM (example), 2954
VSM (notation), 2955
VSP (example), 2956
VSP (subsection, section MO), 2957
VSP (subsection, section VO), 2958
VSP (subsection, section VS), 2959
VSPCV (theorem), 2960
VSPM (theorem), 2961
VSPUD (example), 2962
VSS (example), 2963
W (archetype), 2964
WILA (section), 2965
X (archetype), 2966
Z (Property), 2967
ZC (Property), 2968
ZCN (Property), 2969
ZCV (definition), 2970
ZCV (notation), 2971
zero
complex numbers
Property ZCN, 2972
field
Property ZF, 2973
zero column vector
definition ZCV, 2974
notation, 2975
zero matrix
notation, 2976
zero vector
column vectors
Property ZC, 2977
matrices
Property ZM, 2978
unique
theorem ZVU, 2979
vectors
Property Z, 2980
ZF (Property), 2981
ZM (definition), 2982
ZM (notation), 2983
ZM (Property), 2984
ZNDAB (example), 2985
ZSSM (theorem), 2986
ZVSM (theorem), 2987
ZVU (theorem), 2988