B (archetype), 97
B (definition), 98
B (section), 99
B (subsection, section B), 100
basis
columns nonsingular matrix
example CABAK, 101
common size
theorem BIS, 102
crazy vector apace
example BC, 103
definition B, 104
matrices
example BM, 105
example BSM22, 106
polynomials
example BP, 107
example BPR, 108
example BSP4, 109
example SVP4, 110
subspace of matrices
example BDM22, 111
BC (example), 112
BCS (theorem), 113
BDE (example), 114
BDM22 (example), 115
best cities
money magazine
example MBC, 116
BIS (theorem), 117
BM (example), 118
BNM (subsection, section B), 119
BNS (theorem), 120
BP (example), 121
BPR (example), 122
BRLT (example), 123
BRS (theorem), 124
BS (theorem), 125
BSCV (subsection, section B), 126
BSM22 (example), 127
BSP4 (example), 128
C (archetype), 129
C (definition), 130
C (notation), 131
C (part), 132
C (Property), 133
C (technique, section PT), 134
CABAK (example), 135
CACN (Property), 136
CAEHW (example), 137
CAF (Property), 138
canonical form
nilpotent linear transformation
example CFNLT, 139
theorem CFNLT, 140
CAV (subsection, section O), 141
Cayley-Hamilton
theorem CHT, 142
CB (section), 143
CB (theorem), 144
CBCV (example), 145
CBM (definition), 146
CBM (subsection, section CB), 147
CBP (example), 148
CC (Property), 149
CCCV (definition), 150
CCCV (notation), 151
CCM (definition), 152
CCM (example), 153
CCM (notation), 154
CCM (theorem), 155
CCN (definition), 156
CCN (notation), 157
CCN (subsection, section CNO), 158
CCRA (theorem), 159
CCRM (theorem), 160
CCT (theorem), 161
CD (subsection, section DM), 162
CD (technique, section PT), 163
CEE (subsection, section EE), 164
CELT (example), 165
CELT (subsection, section CB), 166
CEMS6 (example), 167
CF (section), 168
CFDVS (theorem), 169
CFNLT (example), 170
CFNLT (subsection, section NLT), 171
CFNLT (theorem), 172
CFV (example), 173
change of basis
between polynomials
example CBP, 174
change-of-basis
between column vectors
example CBCV, 175
matrix representation
theorem MRCB, 176
similarity
theorem SCB, 177
theorem CB, 178
change-of-basis matrix
definition CBM, 179
inverse
theorem ICBM, 180
characteristic polynomial
definition CP, 181
degree
theorem DCP, 182
size 3 matrix
example CPMS3, 183
CHT (subsection, section JCF), 184
CHT (theorem), 185
CILT (subsection, section ILT), 186
CILTI (theorem), 187
CIM (subsection, section MISLE), 188
CINM (theorem), 189
CIVLT (example), 190
CIVLT (theorem), 191
CLI (theorem), 192
CLTLT (theorem), 193
CM (definition), 194
CM (Property), 195
CM32 (example), 196
CMCN (Property), 197
CMF (Property), 198
CMI (example), 199
CMIAB (example), 200
CMVEI (theorem), 201
CN (appendix), 202
CNA (definition), 203
CNA (notation), 204
CNA (subsection, section CNO), 205
CNE (definition), 206
CNE (notation), 207
CNM (definition), 208
CNM (notation), 209
CNMB (theorem), 210
CNO (section), 211
CNS1 (example), 212
CNS2 (example), 213
CNSV (example), 214
COB (theorem), 215
coefficient matrix
definition CM, 216
nonsingular
theorem SNCM, 217
column space
as null space
theorem FS, 218
Archetype A
example CSAA, 219
Archetype B
example CSAB, 220
as null space
example CSANS, 221
as null space, Archetype G
example FSAG, 222
as row space
theorem CSRST, 223
basis
theorem BCS, 224
consistent system
theorem CSCS, 225
consistent systems
example CSMCS, 226
isomorphic to range, 227
matrix, 228
nonsingular matrix
theorem CSNM, 229
notation, 230
original columns, Archetype D
example CSOCD, 231
row operations, Archetype I
example CSROI, 232
subspace
theorem CSMS, 233
testing membership
example MCSM, 234
two computations
example CSTW, 235
column vector addition
notation, 236
column vector scalar multiplication
notation, 237
commutativity
column vectors
Property CC, 238
matrices
Property CM, 239
vectors
Property C, 240
complex -space
example VSCV, 241
complex arithmetic
example ACN, 242
complex number
conjugate
example CSCN, 243
modulus
example MSCN, 244
complex number
conjugate
definition CCN, 245
modulus
definition MCN, 246
complex numbers
addition
definition CNA, 247
notation, 248
arithmetic properties
theorem PCNA, 249
equality
definition CNE, 250
notation, 251
multiplication
definition CNM, 252
notation, 253
complex vector space
dimension
theorem DCM, 254
composition
injective linear transformations
theorem CILTI, 255
surjective linear transformations
theorem CSLTS, 256
conjugate
addition
theorem CCRA, 257
column vector
definition CCCV, 258
matrix
definition CCM, 259
notation, 260
multiplication
theorem CCRM, 261
notation, 262
of conjugate of a matrix
theorem CCM, 263
scalar multiplication
theorem CRSM, 264
twice
theorem CCT, 265
vector addition
theorem CRVA, 266
conjugate of a vector
notation, 267
conjugation
matrix addition
theorem CRMA, 268
matrix scalar multiplication
theorem CRMSM, 269
matrix transpose
theorem MCT, 270
consistent linear system, 271
consistent linear systems
theorem CSRN, 272
consistent system
definition CS, 273
constructive proofs
technique C, 274
contradiction
technique CD, 275
contrapositive
technique CP, 276
converse
technique CV, 277
coordinates
orthonormal basis
theorem COB, 278
coordinatization
linear combination of matrices
example CM32, 279
linear independence
theorem CLI, 280
orthonormal basis
example CROB3, 281
example CROB4, 282
spanning sets
theorem CSS, 283
coordinatization principle, 284
coordinatizing
polynomials
example CP2, 285
COV (example), 286
COV (subsection, section LDS), 287
CP (definition), 288
CP (subsection, section VR), 289
CP (technique, section PT), 290
CP2 (example), 291
CPMS3 (example), 292
CPSM (theorem), 293
crazy vector space
example CVSR, 294
properties
example PCVS, 295
CRMA (theorem), 296
CRMSM (theorem), 297
CRN (theorem), 298
CROB3 (example), 299
CROB4 (example), 300
CRS (section), 301
CRS (subsection, section FS), 302
CRSM (theorem), 303
CRVA (theorem), 304
CS (definition), 305
CS (example), 306
CS (subsection, section TSS), 307
CSAA (example), 308
CSAB (example), 309
CSANS (example), 310
CSCN (example), 311
CSCS (theorem), 312
CSIP (example), 313
CSLT (subsection, section SLT), 314
CSLTS (theorem), 315
CSM (definition), 316
CSM (notation), 317
CSMCS (example), 318
CSMS (theorem), 319
CSNM (subsection, section CRS), 320
CSNM (theorem), 321
CSOCD (example), 322
CSRN (theorem), 323
CSROI (example), 324
CSRST (theorem), 325
CSS (theorem), 326
CSSE (subsection, section CRS), 327
CSSOC (subsection, section CRS), 328
CSTW (example), 329
CTD (subsection, section TD), 330
CTLT (example), 331
CUMOS (theorem), 332
curve fitting
polynomial through 5 points
example PTFP, 333
CV (definition), 334
CV (notation), 335
CV (technique, section PT), 336
CVA (definition), 337
CVA (notation), 338
CVC (notation), 339
CVE (definition), 340
CVE (notation), 341
CVS (example), 342
CVS (subsection, section VR), 343
CVSM (definition), 344
CVSM (example), 345
CVSM (notation), 346
CVSR (example), 347
D (acronyms, section PDM), 348
D (archetype), 349
D (chapter), 350
D (definition), 351
D (notation), 352
D (section), 353
D (subsection, section D), 354
D (subsection, section SD), 355
D (technique, section PT), 356
D33M (example), 357
DAB (example), 358
DC (example), 359
DC (technique, section PT), 360
DC (theorem), 361
DCM (theorem), 362
DCN (Property), 363
DCP (theorem), 364
DD (subsection, section DM), 365
DEC (theorem), 366
decomposition
technique DC, 367
DED (theorem), 368
definition
A, 369
AM, 370
AME, 371
B, 372
C, 373
CBM, 374
CCCV, 375
CCM, 376
CCN, 377
CM, 378
CNA, 379
CNE, 380
CNM, 381
CP, 382
CS, 383
CSM, 384
CV, 385
CVA, 386
CVE, 387
CVSM, 388
D, 389
DIM, 390
DM, 391
DS, 392
DZM, 393
EEF, 394
EELT, 395
EEM, 396
ELEM, 397
EM, 398
EO, 399
ES, 400
ESYS, 401
F, 402
GES, 403
GEV, 404
GME, 405
HI, 406
HID, 407
HM, 408
HP, 409
HS, 410
IDLT, 411
IDV, 412
IE, 413
ILT, 414
IM, 415
IMP, 416
IP, 417
IS, 418
IVLT, 419
IVS, 420
JB, 421
JCF, 422
KLT, 423
LC, 424
LCCV, 425
LI, 426
LICV, 427
LNS, 428
LSMR, 429
LSS, 430
LT, 431
LTA, 432
LTC, 433
LTM, 434
LTR, 435
LTSM, 436
M, 437
MA, 438
MCN, 439
ME, 440
MI, 441
MM, 442
MR, 443
MSM, 444
MVP, 445
NLT, 446
NM, 447
NOLT, 448
NOM, 449
NRML, 450
NSM, 451
NV, 452
ONS, 453
OSV, 454
OV, 455
PI, 456
PSM, 457
REM, 458
RLD, 459
RLDCV, 460
RLT, 461
RO, 462
ROLT, 463
ROM, 464
RR, 465
RREF, 466
RSM, 467
S, 468
SC, 469
SE, 470
SET, 471
SI, 472
SIM, 473
SLE, 474
SLT, 475
SM, 476
SOLV, 477
SQM, 478
SRM, 479
SS, 480
SSCV, 481
SSET, 482
SU, 483
SUV, 484
SV, 485
SYM, 486
T, 487
technique D, 488
TM, 489
TS, 490
TSHSE, 491
TSVS, 492
UM, 493
UTM, 494
VM, 495
VOC, 496
VR, 497
VS, 498
VSCV, 499
VSM, 500
ZCV, 501
ZM, 502
DEHD (example), 503
DEM (theorem), 504
DEMMM (theorem), 505
DEMS5 (example), 506
DER (theorem), 507
DERC (theorem), 508
determinant
computed two ways
example TCSD, 509
definition DM, 510
equal rows or columns
theorem DERC, 511
expansion, columns
theorem DEC, 512
expansion, rows
theorem DER, 513
identity matrix
theorem DIM, 514
matrix multiplication
theorem DRMM, 515
nonsingular matrix, 516
notation, 517
row or column multiple
theorem DRCM, 518
row or column swap
theorem DRCS, 519
size 2 matrix
theorem DMST, 520
size 3 matrix
example D33M, 521
transpose
theorem DT, 522
via row operations
example DRO, 523
zero
theorem SMZD, 524
zero row or column
theorem DZRC, 525
zero versus nonzero
example ZNDAB, 526
determinant, upper triangular matrix
example DUTM, 527
determinants
elementary matrices
theorem DEMMM, 528
DF (Property), 529
DF (subsection, section CF), 530
DFS (subsection, section PD), 531
DFS (theorem), 532
DGES (theorem), 533
diagonal matrix
definition DIM, 534
diagonalizable
definition DZM, 535
distinct eigenvalues
example DEHD, 536
theorem DED, 537
full eigenspaces
theorem DMFE, 538
not
example NDMS4, 539
diagonalizable matrix
high power
example HPDM, 540
diagonalization
Archetype B
example DAB, 541
criteria
theorem DC, 542
example DMS3, 543
DIM (definition), 544
DIM (theorem), 545
dimension
crazy vector space
example DC, 546
definition D, 547
notation, 548
polynomial subspace
example DSP4, 549
proper subspaces
theorem PSSD, 550
subspace
example DSM22, 551
direct sum
decomposing zero vector
theorem DSZV, 552
definition DS, 553
dimension
theorem DSD, 554
example SDS, 555
from a basis
theorem DSFB, 556
from one subspace
theorem DSFOS, 557
notation, 558
zero intersection
theorem DSZI, 559
direct sums
linear independence
theorem DSLI, 560
repeated
theorem RDS, 561
distributivity
complex numbers
Property DCN, 562
field
Property DF, 563
distributivity, matrix addition
matrices
Property DMAM, 564
distributivity, scalar addition
column vectors
Property DSAC, 565
matrices
Property DSAM, 566
vectors
Property DSA, 567
distributivity, vector addition
column vectors
Property DVAC, 568
vectors
Property DVA, 569
DLDS (theorem), 570
DM (definition), 571
DM (notation), 572
DM (section), 573
DM (theorem), 574
DMAM (Property), 575
DMFE (theorem), 576
DMHP (subsection, section HP), 577
DMHP (theorem), 578
DMMP (theorem), 579
DMS3 (example), 580
DMST (theorem), 581
DNLT (theorem), 582
DNMMM (subsection, section PDM), 583
DP (theorem), 584
DRCM (theorem), 585
DRCMA (theorem), 586
DRCS (theorem), 587
DRMM (theorem), 588
DRO (example), 589
DRO (subsection, section PDM), 590
DROEM (subsection, section PDM), 591
DS (definition), 592
DS (notation), 593
DS (subsection, section PD), 594
DSA (Property), 595
DSAC (Property), 596
DSAM (Property), 597
DSD (theorem), 598
DSFB (theorem), 599
DSFOS (theorem), 600
DSLI (theorem), 601
DSM22 (example), 602
DSP4 (example), 603
DSZI (theorem), 604
DSZV (theorem), 605
DT (theorem), 606
DUTM (example), 607
DVA (Property), 608
DVAC (Property), 609
DVM (theorem), 610
DVS (subsection, section D), 611
DZM (definition), 612
DZRC (theorem), 613
E (acronyms, section SD), 614
E (archetype), 615
E (chapter), 616
E (technique, section PT), 617
ECEE (subsection, section EE), 618
EDELI (theorem), 619
EDYES (theorem), 620
EE (section), 621
EEE (subsection, section EE), 622
EEF (definition), 623
EEF (subsection, section FS), 624
EELT (definition), 625
EELT (subsection, section CB), 626
EEM (definition), 627
EEM (subsection, section EE), 628
EEMAP (theorem), 629
EENS (example), 630
EER (theorem), 631
EESR (theorem), 632
EHM (subsection, section PEE), 633
eigenspace
as null space
theorem EMNS, 634
definition EM, 635
invariant subspace
theorem EIS, 636
subspace
theorem EMS, 637
eigenvalue
algebraic multiplicity
definition AME, 638
complex
example CEMS6, 639
definition EEM, 640
existence
example CAEHW, 641
theorem EMHE, 642
geometric multiplicity
definition GME, 643
index, 644
linear transformation
definition EELT, 645
multiplicities
example EMMS4, 646
power
theorem EOMP, 647
root of characteristic polynomial
theorem EMRCP, 648
scalar multiple
theorem ESMM, 649
symmetric matrix
example ESMS4, 650
zero
theorem SMZE, 651
eigenvalues
building desired
example BDE, 652
complex, of a linear transformation
example CELT, 653
conjugate pairs
theorem ERMCP, 654
distinct
example DEMS5, 655
example SEE, 656
Hermitian matrices
theorem HMRE, 657
inverse
theorem EIM, 658
maximum number
theorem MNEM, 659
multiplicities
example HMEM5, 660
theorem ME, 661
number
theorem NEM, 662
of a polynomial
theorem EPM, 663
size 3 matrix
example EMS3, 664
example ESMS3, 665
transpose
theorem ETM, 666
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 667
eigenvector, 668
linear transformation, 669
eigenvectors, 670
conjugate pairs, 671
Hermitian matrices
theorem HMOE, 672
linear transformation
example ELTBM, 673
example ELTBP, 674
linearly independent
theorem EDELI, 675
of a linear transformation
example ELTT, 676
EILT (subsection, section ILT), 677
EIM (theorem), 678
EIS (example), 679
EIS (theorem), 680
ELEM (definition), 681
ELEM (notation), 682
elementary matrices
definition ELEM, 683
determinants
theorem DEM, 684
nonsingular
theorem EMN, 685
notation, 686
row operations
example EMRO, 687
theorem EMDRO, 688
ELIS (theorem), 689
ELTBM (example), 690
ELTBP (example), 691
ELTT (example), 692
EM (definition), 693
EM (subsection, section DM), 694
EMDRO (theorem), 695
EMHE (theorem), 696
EMMS4 (example), 697
EMMVP (theorem), 698
EMN (theorem), 699
EMNS (theorem), 700
EMP (theorem), 701
empty set, 702
notation, 703
EMRCP (theorem), 704
EMRO (example), 705
EMS (theorem), 706
EMS3 (example), 707
ENLT (theorem), 708
EO (definition), 709
EOMP (theorem), 710
EOPSS (theorem), 711
EPM (theorem), 712
EPSM (theorem), 713
equal matrices
via equal matrix-vector products
theorem EMMVP, 714
equation operations
definition EO, 715
theorem EOPSS, 716
equivalence statements
technique E, 717
equivalences
technique ME, 718
equivalent systems
definition ESYS, 719
ERMCP (theorem), 720
ES (definition), 721
ES (notation), 722
ESEO (subsection, section SSLE), 723
ESLT (subsection, section SLT), 724
ESMM (theorem), 725
ESMS3 (example), 726
ESMS4 (example), 727
ESYS (definition), 728
ETM (theorem), 729
EVS (subsection, section VS), 730
example
AALC, 731
ABLC, 732
ABS, 733
ACN, 734
AHSAC, 735
AIVLT, 736
ALT, 737
ALTMM, 738
AM, 739
AMAA, 740
ANILT, 741
ANM, 742
AOS, 743
ASC, 744
AVR, 745
BC, 746
BDE, 747
BDM22, 748
BM, 749
BP, 750
BPR, 751
BRLT, 752
BSM22, 753
BSP4, 754
CABAK, 755
CAEHW, 756
CBCV, 757
CBP, 758
CCM, 759
CELT, 760
CEMS6, 761
CFNLT, 762
CFV, 763
CIVLT, 764
CM32, 765
CMI, 766
CMIAB, 767
CNS1, 768
CNS2, 769
CNSV, 770
COV, 771
CP2, 772
CPMS3, 773
CROB3, 774
CROB4, 775
CS, 776
CSAA, 777
CSAB, 778
CSANS, 779
CSCN, 780
CSIP, 781
CSMCS, 782
CSOCD, 783
CSROI, 784
CSTW, 785
CTLT, 786
CVS, 787
CVSM, 788
CVSR, 789
D33M, 790
DAB, 791
DC, 792
DEHD, 793
DEMS5, 794
DMS3, 795
DRO, 796
DSM22, 797
DSP4, 798
DUTM, 799
EENS, 800
EIS, 801
ELTBM, 802
ELTBP, 803
ELTT, 804
EMMS4, 805
EMRO, 806
EMS3, 807
ESMS3, 808
ESMS4, 809
FDV, 810
FF8, 811
FRAN, 812
FS1, 813
FS2, 814
FSAG, 815
GE4, 816
GE6, 817
GENR6, 818
GSTV, 819
HISAA, 820
HISAD, 821
HMEM5, 822
HP, 823
HPDM, 824
HUSAB, 825
IAP, 826
IAR, 827
IAS, 828
IAV, 829
ILTVR, 830
IM, 831
IM11, 832
IS, 833
ISJB, 834
ISMR4, 835
ISMR6, 836
ISSI, 837
IVSAV, 838
JB4, 839
JCF10, 840
KPNLT, 841
KVMR, 842
LCM, 843
LDCAA, 844
LDHS, 845
LDP4, 846
LDRN, 847
LDS, 848
LIC, 849
LICAB, 850
LIHS, 851
LIM32, 852
LINSB, 853
LIP4, 854
LIS, 855
LLDS, 856
LNS, 857
LTDB1, 858
LTDB2, 859
LTDB3, 860
LTM, 861
LTPM, 862
LTPP, 863
LTRGE, 864
MA, 865
MBC, 866
MCSM, 867
MFLT, 868
MI, 869
MIVS, 870
MMNC, 871
MNSLE, 872
MOLT, 873
MPMR, 874
MRBE, 875
MRCM, 876
MSCN, 877
MSM, 878
MTV, 879
MWIAA, 880
NDMS4, 881
NIAO, 882
NIAQ, 883
NIAQR, 884
NIDAU, 885
NJB5, 886
NKAO, 887
NLT, 888
NM, 889
NM62, 890
NM64, 891
NM83, 892
NRREF, 893
NSAO, 894
NSAQ, 895
NSAQR, 896
NSC2A, 897
NSC2S, 898
NSC2Z, 899
NSDAT, 900
NSDS, 901
NSE, 902
NSEAI, 903
NSLE, 904
NSLIL, 905
NSNM, 906
NSR, 907
NSS, 908
OLTTR, 909
ONFV, 910
ONTV, 911
OSGMD, 912
OSMC, 913
PCVS, 914
PM, 915
PSHS, 916
PTFP, 917
PTM, 918
PTMEE, 919
RAO, 920
RES, 921
RNM, 922
RNSM, 923
ROD2, 924
ROD4, 925
RREF, 926
RREFN, 927
RRTI, 928
RS, 929
RSAI, 930
RSB, 931
RSC5, 932
RSNS, 933
RSREM, 934
RSSC4, 935
RVMR, 936
S, 937
SAA, 938
SAB, 939
SABMI, 940
SAE, 941
SAN, 942
SAR, 943
SAV, 944
SC, 945
SC3, 946
SCAA, 947
SCAB, 948
SCAD, 949
SDS, 950
SEE, 951
SEEF, 952
SETM, 953
SI, 954
SM2Z7, 955
SM32, 956
SMLT, 957
SMS3, 958
SMS5, 959
SP4, 960
SPIAS, 961
SRR, 962
SS, 963
SS6W, 964
SSC, 965
SSET, 966
SSM22, 967
SSNS, 968
SSP, 969
SSP4, 970
STLT, 971
STNE, 972
SU, 973
SUVOS, 974
SVP4, 975
SYM, 976
TCSD, 977
TD4, 978
TDEE6, 979
TDSSE, 980
TIS, 981
TIVS, 982
TKAP, 983
TLC, 984
TM, 985
TMP, 986
TOV, 987
TREM, 988
TTS, 989
UM3, 990
UPM, 991
US, 992
USR, 993
VA, 994
VESE, 995
VFS, 996
VFSAD, 997
VFSAI, 998
VFSAL, 999
VM4, 1000
VRC4, 1001
VRP2, 1002
VSCV, 1003
VSF, 1004
VSIM5, 1005
VSIS, 1006
VSM, 1007
VSP, 1008
VSPUD, 1009
VSS, 1010
ZNDAB, 1011
EXC (subsection, section B), 1012
EXC (subsection, section CB), 1013
EXC (subsection, section CF), 1014
EXC (subsection, section CRS), 1015
EXC (subsection, section D), 1016
EXC (subsection, section DM), 1017
EXC (subsection, section EE), 1018
EXC (subsection, section F), 1019
EXC (subsection, section FS), 1020
EXC (subsection, section HP), 1021
EXC (subsection, section HSE), 1022
EXC (subsection, section ILT), 1023
EXC (subsection, section IVLT), 1024
EXC (subsection, section LC), 1025
EXC (subsection, section LDS), 1026
EXC (subsection, section LI), 1027
EXC (subsection, section LISS), 1028
EXC (subsection, section LT), 1029
EXC (subsection, section MINM), 1030
EXC (subsection, section MISLE), 1031
EXC (subsection, section MM), 1032
EXC (subsection, section MO), 1033
EXC (subsection, section MR), 1034
EXC (subsection, section NM), 1035
EXC (subsection, section O), 1036
EXC (subsection, section PD), 1037
EXC (subsection, section PDM), 1038
EXC (subsection, section PEE), 1039
EXC (subsection, section PSM), 1040
EXC (subsection, section RREF), 1041
EXC (subsection, section S), 1042
EXC (subsection, section SD), 1043
EXC (subsection, section SLT), 1044
EXC (subsection, section SS), 1045
EXC (subsection, section SSLE), 1046
EXC (subsection, section T), 1047
EXC (subsection, section TSS), 1048
EXC (subsection, section VO), 1049
EXC (subsection, section VR), 1050
EXC (subsection, section VS), 1051
EXC (subsection, section WILA), 1052
extended echelon form
submatrices
example SEEF, 1053
extended reduced row-echelon form
properties
theorem PEEF, 1054
F (archetype), 1055
F (definition), 1056
F (section), 1057
F (subsection, section F), 1058
FDV (example), 1059
FF (subsection, section F), 1060
FF8 (example), 1061
field
definition F, 1062
FIMP (theorem), 1063
finite field
size 8
example FF8, 1064
four subsets
example FS1, 1065
example FS2, 1066
four subspaces
dimension
theorem DFS, 1067
FRAN (example), 1068
free variables
example CFV, 1069
free variables, number
theorem FVCS, 1070
free, independent variables
example FDV, 1071
FS (section), 1072
FS (subsection, section FS), 1073
FS (subsection, section SD), 1074
FS (theorem), 1075
FS1 (example), 1076
FS2 (example), 1077
FSAG (example), 1078
FTMR (theorem), 1079
FV (subsection, section TSS), 1080
FVCS (theorem), 1081
G (archetype), 1082
G (theorem), 1083
GE4 (example), 1084
GE6 (example), 1085
GEE (subsection, section IS), 1086
GEK (theorem), 1087
generalized eigenspace
as kernel
theorem GEK, 1088
definition GES, 1089
dimension
theorem DGES, 1090
dimension 4 domain
example GE4, 1091
dimension 6 domain
example GE6, 1092
invariant subspace
theorem GESIS, 1093
nilpotent restriction
theorem RGEN, 1094
nilpotent restrictions, dimension 6 domain
example GENR6, 1095
notation, 1096
generalized eigenspace decomposition
theorem GESD, 1097
generalized eigenvector
definition GEV, 1098
GENR6 (example), 1099
GES (definition), 1100
GES (notation), 1101
GESD (subsection, section JCF), 1102
GESD (theorem), 1103
GESIS (theorem), 1104
GEV (definition), 1105
GFDL (appendix), 1106
GME (definition), 1107
goldilocks
theorem G, 1108
Gram-Schmidt
column vectors
theorem GSP, 1109
three vectors
example GSTV, 1110
gram-schmidt
mathematica, 1111
GS (technique, section PT), 1112
GSP (subsection, section O), 1113
GSP (theorem), 1114
GSP.MMA (computation, section MMA), 1115
GSTV (example), 1116
GT (subsection, section PD), 1117
H (archetype), 1118
Hadamard Identity
notation, 1119
Hadamard identity
definition HID, 1120
Hadamard Inverse
notation, 1121
Hadamard inverse
definition HI, 1122
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1123
notation, 1124
Hadamard product
commutativity
theorem HPC, 1125
definition HP, 1126
diagonal matrices
theorem DMMP, 1127
distributivity
theorem HPDAA, 1128
example HP, 1129
identity
theorem HPHID, 1130
inverse
theorem HPHI, 1131
scalar matrix multiplication
theorem HPSMM, 1132
hermitian
definition HM, 1133
Hermitian matrix
inner product
theorem HMIP, 1134
HI (definition), 1135
HI (notation), 1136
HID (definition), 1137
HID (notation), 1138
HISAA (example), 1139
HISAD (example), 1140
HM (definition), 1141
HM (subsection, section MM), 1142
HMEM5 (example), 1143
HMIP (theorem), 1144
HMOE (theorem), 1145
HMRE (theorem), 1146
HMVEI (theorem), 1147
homogeneous system
consistent
theorem HSC, 1148
definition HS, 1149
infinitely many solutions
theorem HMVEI, 1150
homogeneous systems
linear independence, 1151
homogenous system
Archetype C
example AHSAC, 1152
HP (definition), 1153
HP (example), 1154
HP (notation), 1155
HP (section), 1156
HPC (theorem), 1157
HPDAA (theorem), 1158
HPDM (example), 1159
HPHI (theorem), 1160
HPHID (theorem), 1161
HPSMM (theorem), 1162
HS (definition), 1163
HSC (theorem), 1164
HSE (section), 1165
HUSAB (example), 1166
I (archetype), 1167
I (technique, section PT), 1168
IAP (example), 1169
IAR (example), 1170
IAS (example), 1171
IAV (example), 1172
ICBM (theorem), 1173
ICLT (theorem), 1174
identities
technique PI, 1175
identity matrix
determinant, 1176
example IM, 1177
notation, 1178
IDLT (definition), 1179
IDV (definition), 1180
IE (definition), 1181
IE (notation), 1182
IFDVS (theorem), 1183
IILT (theorem), 1184
ILT (definition), 1185
ILT (section), 1186
ILTB (theorem), 1187
ILTD (subsection, section ILT), 1188
ILTD (theorem), 1189
ILTIS (theorem), 1190
ILTLI (subsection, section ILT), 1191
ILTLI (theorem), 1192
ILTLT (theorem), 1193
ILTVR (example), 1194
IM (definition), 1195
IM (example), 1196
IM (notation), 1197
IM (subsection, section MISLE), 1198
IM11 (example), 1199
IMILT (theorem), 1200
IMP (definition), 1201
IMR (theorem), 1202
inconsistent linear systems
theorem ISRN, 1203
independent, dependent variables
definition IDV, 1204
indesxstring
example SM2Z7, 1205
example SSET, 1206
index
eigenvalue
definition IE, 1207
notation, 1208
indexstring
theorem DRCMA, 1209
theorem OBUTR, 1210
theorem UMCOB, 1211
induction
technique I, 1212
infinite solution set
example ISSI, 1213
infinite solutions,
example IS, 1214
injective
example IAP, 1215
example IAR, 1216
not
example NIAO, 1217
example NIAQ, 1218
example NIAQR, 1219
not, by dimension
example NIDAU, 1220
polynomials to matrices
example IAV, 1221
injective linear transformation
bases
theorem ILTB, 1222
injective linear transformations
dimension
theorem ILTD, 1223
inner product
anti-commutative
theorem IPAC, 1224
example CSIP, 1225
norm
theorem IPN, 1226
notation, 1227
positive
theorem PIP, 1228
scalar multiplication
theorem IPSM, 1229
vector addition
theorem IPVA, 1230
integers
mod
definition IMP, 1231
mod , field
theorem FIMP, 1232
mod 11
example IM11, 1233
interpolating polynomial
theorem IP, 1234
invariant subspace
definition IS, 1235
eigenspace, 1236
eigenspaces
example EIS, 1237
example TIS, 1238
Jordan block
example ISJB, 1239
kernels of powers
theorem KPIS, 1240
inverse
composition of linear transformations
theorem ICLT, 1241
example CMI, 1242
example MI, 1243
notation, 1244
of a matrix, 1245
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1246
invertible linear transformations
composition
theorem CIVLT, 1247
computing
example CIVLT, 1248
IP (definition), 1249
IP (notation), 1250
IP (subsection, section O), 1251
IP (theorem), 1252
IPAC (theorem), 1253
IPN (theorem), 1254
IPSM (theorem), 1255
IPVA (theorem), 1256
IS (definition), 1257
IS (example), 1258
IS (section), 1259
IS (subsection, section IS), 1260
ISJB (example), 1261
ISMR4 (example), 1262
ISMR6 (example), 1263
isomorphic
multiple vector spaces
example MIVS, 1264
vector spaces
example IVSAV, 1265
isomorphic vector spaces
dimension
theorem IVSED, 1266
example TIVS, 1267
ISRN (theorem), 1268
ISSI (example), 1269
ITMT (theorem), 1270
IV (subsection, section IVLT), 1271
IVLT (definition), 1272
IVLT (section), 1273
IVLT (subsection, section IVLT), 1274
IVLT (subsection, section MR), 1275
IVS (definition), 1276
IVSAV (example), 1277
IVSED (theorem), 1278
J (archetype), 1279
JB (definition), 1280
JB (notation), 1281
JB4 (example), 1282
JCF (definition), 1283
JCF (section), 1284
JCF (subsection, section JCF), 1285
JCF10 (example), 1286
JCFLT (theorem), 1287
Jordan block
definition JB, 1288
nilpotent
theorem NJB, 1289
notation, 1290
size 4
example JB4, 1291
Jordan canonical form
definition JCF, 1292
size 10
example JCF10, 1293
K (archetype), 1294
kernel
injective linear transformation
theorem KILT, 1295
isomorphic to null space
theorem KNSI, 1296
linear transformation
example NKAO, 1297
notation, 1298
of a linear transformation
definition KLT, 1299
pre-image, 1300
subspace
theorem KLTS, 1301
trivial
example TKAP, 1302
via matrix representation
example KVMR, 1303
KILT (theorem), 1304
KLT (definition), 1305
KLT (notation), 1306
KLT (subsection, section ILT), 1307
KLTS (theorem), 1308
KNSI (theorem), 1309
KPI (theorem), 1310
KPIS (theorem), 1311
KPLT (theorem), 1312
KPNLT (example), 1313
KPNLT (theorem), 1314
KVMR (example), 1315
L (archetype), 1316
L (technique, section PT), 1317
LA (subsection, section WILA), 1318
LC (definition), 1319
LC (section), 1320
LC (subsection, section LC), 1321
LC (technique, section PT), 1322
LCCV (definition), 1323
LCM (example), 1324
LDCAA (example), 1325
LDHS (example), 1326
LDP4 (example), 1327
LDRN (example), 1328
LDS (example), 1329
LDS (section), 1330
LDSS (subsection, section LDS), 1331
least squares
minimizes residuals
theorem LSMR, 1332
least squares solution
definition LSS, 1333
left null space
as row space, 1334
definition LNS, 1335
example LNS, 1336
notation, 1337
subspace
theorem LNSMS, 1338
lemma
technique LC, 1339
LI (definition), 1340
LI (section), 1341
LI (subsection, section LISS), 1342
LIC (example), 1343
LICAB (example), 1344
LICV (definition), 1345
LIHS (example), 1346
LIM32 (example), 1347
linear combination
system of equations
example ABLC, 1348
definition LC, 1349
definition LCCV, 1350
example TLC, 1351
linear transformation, 1352
matrices
example LCM, 1353
system of equations
example AALC, 1354
linear combinations
solutions to linear systems
theorem SLSLC, 1355
linear dependence
more vectors than size
theorem MVSLD, 1356
linear independence
definition LI, 1357
definition LICV, 1358
homogeneous systems
theorem LIVHS, 1359
injective linear transformation
theorem ILTLI, 1360
matrices
example LIM32, 1361
orthogonal, 1362
r and n
theorem LIVRN, 1363
linear solve
mathematica, 1364
linear system
consistent
theorem RCLS, 1365
matrix representation
definition LSMR, 1366
notation, 1367
linear systems
notation
example MNSLE, 1368
example NSLE, 1369
linear transformation
polynomials to polynomials
example LTPP, 1370
addition
definition LTA, 1371
theorem MLTLT, 1372
theorem SLTLT, 1373
as matrix multiplication
example ALTMM, 1374
basis of range
example BRLT, 1375
checking
example ALT, 1376
composition
definition LTC, 1377
theorem CLTLT, 1378
defined by a matrix
example LTM, 1379
defined on a basis
example LTDB1, 1380
example LTDB2, 1381
example LTDB3, 1382
theorem LTDB, 1383
definition LT, 1384
identity
definition IDLT, 1385
injection
definition ILT, 1386
inverse
theorem ILTLT, 1387
inverse of inverse
theorem IILT, 1388
invertible
definition IVLT, 1389
example AIVLT, 1390
invertible, injective and surjective
theorem ILTIS, 1391
Jordan canonical form
theorem JCFLT, 1392
kernels of powers
theorem KPLT, 1393
linear combination
theorem LTLC, 1394
matrix of, 1395
example MFLT, 1396
example MOLT, 1397
not
example NLT, 1398
not invertible
example ANILT, 1399
notation, 1400
polynomials to matrices
example LTPM, 1401
rank plus nullity
theorem RPNDD, 1402
restriction
definition LTR, 1403
notation, 1404
scalar multiple
example SMLT, 1405
scalar multiplication
definition LTSM, 1406
spanning range
theorem SSRLT, 1407
sum
example STLT, 1408
surjection
definition SLT, 1409
vector space of, 1410
zero vector
theorem LTTZZ, 1411
linear transformation inverse
via matrix representation
example ILTVR, 1412
linear transformation restriction
on generalized eigenspace
example LTRGE, 1413
linear transformations
compositions
example CTLT, 1414
from matrices
theorem MBLT, 1415
linearly dependent
example LDRN, 1416
via homogeneous system
example LDHS, 1417
linearly dependent columns
Archetype A
example LDCAA, 1418
linearly dependent set
example LDS, 1419
linear combinations within
theorem DLDS, 1420
polynomials
example LDP4, 1421
linearly independent
crazy vector space
example LIC, 1422
extending sets
theorem ELIS, 1423
polynomials
example LIP4, 1424
via homogeneous system
example LIHS, 1425
linearly independent columns
Archetype B
example LICAB, 1426
linearly independent set
example LIS, 1427
example LLDS, 1428
LINM (subsection, section LI), 1429
LINSB (example), 1430
LIP4 (example), 1431
LIS (example), 1432
LISS (section), 1433
LISV (subsection, section LI), 1434
LIVHS (theorem), 1435
LIVRN (theorem), 1436
LLDS (example), 1437
LNS (definition), 1438
LNS (example), 1439
LNS (notation), 1440
LNS (subsection, section FS), 1441
LNSMS (theorem), 1442
lower triangular matrix
definition LTM, 1443
LS.MMA (computation, section MMA), 1444
LSMR (definition), 1445
LSMR (notation), 1446
LSMR (theorem), 1447
LSS (definition), 1448
LT (acronyms, section IVLT), 1449
LT (chapter), 1450
LT (definition), 1451
LT (notation), 1452
LT (section), 1453
LT (subsection, section LT), 1454
LTA (definition), 1455
LTC (definition), 1456
LTC (subsection, section LT), 1457
LTDB (theorem), 1458
LTDB1 (example), 1459
LTDB2 (example), 1460
LTDB3 (example), 1461
LTLC (subsection, section LT), 1462
LTLC (theorem), 1463
LTM (definition), 1464
LTM (example), 1465
LTPM (example), 1466
LTPP (example), 1467
LTR (definition), 1468
LTR (notation), 1469
LTRGE (example), 1470
LTSM (definition), 1471
LTTZZ (theorem), 1472
M (acronyms, section FS), 1473
M (archetype), 1474
M (chapter), 1475
M (definition), 1476
M (notation), 1477
MA (definition), 1478
MA (example), 1479
MA (notation), 1480
MACN (Property), 1481
MAF (Property), 1482
MAP (subsection, section SVD), 1483
mathematica
gram-schmidt (computation), 1484
linear solve (computation), 1485
matrix entry (computation), 1486
matrix inverse (computation), 1487
matrix multiplication (computation), 1488
null space (computation), 1489
row reduce (computation), 1490
transpose of a matrix (computation), 1491
vector form of solutions (computation), 1492
vector linear combinations (computation), 1493
mathematical language
technique L, 1494
matrix
addition
definition MA, 1495
notation, 1496
augmented
definition AM, 1497
column space
definition CSM, 1498
complex conjugate
example CCM, 1499
definition M, 1500
equality
definition ME, 1501
notation, 1502
example AM, 1503
identity
definition IM, 1504
inverse
definition MI, 1505
nonsingular
definition NM, 1506
notation, 1507
of a linear transformation
theorem MLTCV, 1508
product
example PTM, 1509
example PTMEE, 1510
product with vector
definition MVP, 1511
rectangular, 1512
row space
definition RSM, 1513
scalar multiplication
definition MSM, 1514
notation, 1515
singular, 1516
square
definition SQM, 1517
submatrices
example SS, 1518
submatrix
definition SM, 1519
symmetric
definition SYM, 1520
transpose
definition TM, 1521
unitary
definition UM, 1522
unitary is invertible
theorem UMI, 1523
zero
definition ZM, 1524
matrix addition
example MA, 1525
matrix components
notation, 1526
matrix entry
mathematica, 1527
ti83, 1528
ti86, 1529
matrix inverse
Archetype B, 1530
computation
theorem CINM, 1531
mathematica, 1532
nonsingular matrix
theorem NI, 1533
of a matrix inverse
theorem MIMI, 1534
one-sided
theorem OSIS, 1535
product
theorem SS, 1536
scalar multiple
theorem MISM, 1537
size 2 matrices
theorem TTMI, 1538
transpose
theorem MIT, 1539
uniqueness
theorem MIU, 1540
matrix multiplication
adjoints
theorem MMAD, 1541
associativity
theorem MMA, 1542
complex conjugation
theorem MMCC, 1543
definition MM, 1544
distributivity
theorem MMDAA, 1545
entry-by-entry
theorem EMP, 1546
identity matrix
theorem MMIM, 1547
inner product
theorem MMIP, 1548
mathematica, 1549
noncommutative
example MMNC, 1550
scalar matrix multiplication
theorem MMSMM, 1551
systems of linear equations
theorem SLEMM, 1552
transposes
theorem MMT, 1553
zero matrix
theorem MMZM, 1554
matrix product
as composition of linear transformations
example MPMR, 1555
matrix representation
basis of eigenvectors
example MRBE, 1556
composition of linear transformations
theorem MRCLT, 1557
definition MR, 1558
invertible
theorem IMR, 1559
multiple of a linear transformation
theorem MRMLT, 1560
notation, 1561
restriction to generalized eigenspace
theorem MRRGE, 1562
sum of linear transformations
theorem MRSLT, 1563
theorem FTMR, 1564
upper triangular
theorem UTMR, 1565
matrix representations
converting with change-of-basis
example MRCM, 1566
example OLTTR, 1567
matrix scalar multiplication
example MSM, 1568
matrix vector space
dimension
theorem DM, 1569
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1570
matrix-vector product
example MTV, 1571
notation, 1572
MBC (example), 1573
MBLT (theorem), 1574
MC (notation), 1575
MCC (subsection, section MO), 1576
MCCN (Property), 1577
MCF (Property), 1578
MCN (definition), 1579
MCN (subsection, section CNO), 1580
MCSM (example), 1581
MCT (theorem), 1582
MD (chapter), 1583
ME (definition), 1584
ME (notation), 1585
ME (subsection, section PEE), 1586
ME (technique, section PT), 1587
ME (theorem), 1588
ME.MMA (computation, section MMA), 1589
ME.TI83 (computation, section TI83), 1590
ME.TI86 (computation, section TI86), 1591
MEASM (subsection, section MO), 1592
MFLT (example), 1593
MI (definition), 1594
MI (example), 1595
MI (notation), 1596
MI.MMA (computation, section MMA), 1597
MICN (Property), 1598
MIF (Property), 1599
MIMI (theorem), 1600
MINM (section), 1601
MISLE (section), 1602
MISM (theorem), 1603
MIT (theorem), 1604
MIU (theorem), 1605
MIVS (example), 1606
MLT (subsection, section LT), 1607
MLTCV (theorem), 1608
MLTLT (theorem), 1609
MM (definition), 1610
MM (section), 1611
MM (subsection, section MM), 1612
MM.MMA (computation, section MMA), 1613
MMA (section), 1614
MMA (theorem), 1615
MMAD (theorem), 1616
MMCC (theorem), 1617
MMDAA (theorem), 1618
MMEE (subsection, section MM), 1619
MMIM (theorem), 1620
MMIP (theorem), 1621
MMNC (example), 1622
MMSMM (theorem), 1623
MMT (theorem), 1624
MMZM (theorem), 1625
MNEM (theorem), 1626
MNSLE (example), 1627
MO (section), 1628
MOLT (example), 1629
more variables than equations
example OSGMD, 1630
theorem CMVEI, 1631
MPMR (example), 1632
MR (definition), 1633
MR (notation), 1634
MR (section), 1635
MRBE (example), 1636
MRCB (theorem), 1637
MRCLT (theorem), 1638
MRCM (example), 1639
MRMLT (theorem), 1640
MRRGE (theorem), 1641
MRS (subsection, section CB), 1642
MRSLT (theorem), 1643
MSCN (example), 1644
MSM (definition), 1645
MSM (example), 1646
MSM (notation), 1647
MTV (example), 1648
multiplicative associativity
complex numbers
Property MACN, 1649
multiplicative closure
complex numbers
Property MCCN, 1650
field
Property MCF, 1651
multiplicative commuativity
complex numbers
Property CMCN, 1652
multiplicative inverse
complex numbers
Property MICN, 1653
MVNSE (subsection, section RREF), 1654
MVP (definition), 1655
MVP (notation), 1656
MVP (subsection, section MM), 1657
MVSLD (theorem), 1658
MWIAA (example), 1659
N (archetype), 1660
N (subsection, section O), 1661
N (technique, section PT), 1662
NDMS4 (example), 1663
negation of statements
technique N, 1664
NEM (theorem), 1665
NI (theorem), 1666
NIAO (example), 1667
NIAQ (example), 1668
NIAQR (example), 1669
NIDAU (example), 1670
nilpotent
linear transformation
definition NLT, 1671
NJB (theorem), 1672
NJB5 (example), 1673
NKAO (example), 1674
NLT (definition), 1675
NLT (example), 1676
NLT (section), 1677
NLT (subsection, section NLT), 1678
NLTFO (subsection, section LT), 1679
NM (definition), 1680
NM (example), 1681
NM (section), 1682
NM (subsection, section NM), 1683
NM (subsection, section OD), 1684
NM62 (example), 1685
NM64 (example), 1686
NM83 (example), 1687
NME1 (theorem), 1688
NME2 (theorem), 1689
NME3 (theorem), 1690
NME4 (theorem), 1691
NME5 (theorem), 1692
NME6 (theorem), 1693
NME7 (theorem), 1694
NME8 (theorem), 1695
NME9 (theorem), 1696
NMI (subsection, section MINM), 1697
NMLIC (theorem), 1698
NMPEM (theorem), 1699
NMRRI (theorem), 1700
NMTNS (theorem), 1701
NMUS (theorem), 1702
NOILT (theorem), 1703
NOLT (definition), 1704
NOLT (notation), 1705
NOM (definition), 1706
NOM (notation), 1707
nonsingular
columns as basis
theorem CNMB, 1708
nonsingular matrices
linearly independent columns
theorem NMLIC, 1709
nonsingular matrix
Archetype B
example NM, 1710
column space, 1711
elemntary matrices
theorem NMPEM, 1712
equivalences
theorem NME1, 1713
theorem NME2, 1714
theorem NME3, 1715
theorem NME4, 1716
theorem NME5, 1717
theorem NME6, 1718
theorem NME7, 1719
theorem NME8, 1720
theorem NME9, 1721
matrix inverse, 1722
null space
example NSNM, 1723
nullity, 1724
product of nonsingular matrices
theorem NPNT, 1725
rank
theorem RNNM, 1726
row-reduced
theorem NMRRI, 1727
trivial null space
theorem NMTNS, 1728
unique solutions
theorem NMUS, 1729
nonsingular matrix, row-reduced
example NSR, 1730
norm
example CNSV, 1731
inner product, 1732
notation, 1733
normal matrix
definition NRML, 1734
example ANM, 1735
orthonormal basis, 1736
notation
A, 1737
AM, 1738
C, 1739
CCCV, 1740
CCM, 1741
CCN, 1742
CNA, 1743
CNE, 1744
CNM, 1745
CSM, 1746
CV, 1747
CVA, 1748
CVC, 1749
CVE, 1750
CVSM, 1751
D, 1752
DM, 1753
DS, 1754
ELEM, 1755
ES, 1756
GES, 1757
HI, 1758
HID, 1759
HP, 1760
IE, 1761
IM, 1762
IP, 1763
JB, 1764
KLT, 1765
LNS, 1766
LSMR, 1767
LT, 1768
LTR, 1769
M, 1770
MA, 1771
MC, 1772
ME, 1773
MI, 1774
MR, 1775
MSM, 1776
MVP, 1777
NOLT, 1778
NOM, 1779
NSM, 1780
NV, 1781
RLT, 1782
RO, 1783
ROLT, 1784
ROM, 1785
RREFA, 1786
RSM, 1787
SC, 1788
SE, 1789
SETM, 1790
SI, 1791
SM, 1792
SRM, 1793
SSET, 1794
SSV, 1795
SU, 1796
SUV, 1797
T, 1798
TM, 1799
VR, 1800
VSCV, 1801
VSM, 1802
ZCV, 1803
ZM, 1804
notation for a linear system
example NSE, 1805
NPNT (theorem), 1806
NRFO (subsection, section MR), 1807
NRML (definition), 1808
NRREF (example), 1809
NS.MMA (computation, section MMA), 1810
NSAO (example), 1811
NSAQ (example), 1812
NSAQR (example), 1813
NSC2A (example), 1814
NSC2S (example), 1815
NSC2Z (example), 1816
NSDAT (example), 1817
NSDS (example), 1818
NSE (example), 1819
NSEAI (example), 1820
NSLE (example), 1821
NSLIL (example), 1822
NSM (definition), 1823
NSM (notation), 1824
NSM (subsection, section HSE), 1825
NSMS (theorem), 1826
NSNM (example), 1827
NSNM (subsection, section NM), 1828
NSR (example), 1829
NSS (example), 1830
NSSLI (subsection, section LI), 1831
Null space
as a span
example NSDS, 1832
null space
Archetype I
example NSEAI, 1833
basis
theorem BNS, 1834
computation
example CNS1, 1835
example CNS2, 1836
isomorphic to kernel, 1837
linearly independent basis
example LINSB, 1838
mathematica, 1839
matrix
definition NSM, 1840
nonsingular matrix, 1841
notation, 1842
singular matrix, 1843
spanning set
example SSNS, 1844
theorem SSNS, 1845
subspace
theorem NSMS, 1846
null space span, linearly independent
Archetype L
example NSLIL, 1847
nullity
computing, 1848
injective linear transformation
theorem NOILT, 1849
linear transformation
definition NOLT, 1850
matrix, 1851
definition NOM, 1852
notation, 1853, 1854
square matrix, 1855
NV (definition), 1856
NV (notation), 1857
NVM (theorem), 1858
O (archetype), 1859
O (Property), 1860
O (section), 1861
OBC (subsection, section B), 1862
OBNM (theorem), 1863
OBUTR (theorem), 1864
OC (Property), 1865
OCN (Property), 1866
OD (section), 1867
OD (subsection, section OD), 1868
OD (theorem), 1869
OF (Property), 1870
OLTTR (example), 1871
OM (Property), 1872
one
column vectors
Property OC, 1873
complex numbers
Property OCN, 1874
field
Property OF, 1875
matrices
Property OM, 1876
vectors
Property O, 1877
ONFV (example), 1878
ONS (definition), 1879
ONTV (example), 1880
orthogonal
linear independence
theorem OSLI, 1881
set
example AOS, 1882
set of vectors
definition OSV, 1883
vector pairs
definition OV, 1884
orthogonal vectors
example TOV, 1885
orthonormal
definition ONS, 1886
matrix columns
example OSMC, 1887
orthonormal basis
normal matrix
theorem OBNM, 1888
orthonormal diagonalization
theorem OD, 1889
orthonormal set
four vectors
example ONFV, 1890
three vectors
example ONTV, 1891
OSGMD (example), 1892
OSIS (theorem), 1893
OSLI (theorem), 1894
OSMC (example), 1895
OSV (definition), 1896
OV (definition), 1897
OV (subsection, section O), 1898
P (appendix), 1899
P (archetype), 1900
P (technique, section PT), 1901
particular solutions
example PSHS, 1902
PCNA (theorem), 1903
PCVS (example), 1904
PD (section), 1905
PDM (section), 1906
PDM (theorem), 1907
PEE (section), 1908
PEEF (theorem), 1909
PI (definition), 1910
PI (subsection, section LT), 1911
PI (technique, section PT), 1912
PIP (theorem), 1913
PM (example), 1914
PM (subsection, section EE), 1915
PMI (subsection, section MISLE), 1916
PMM (subsection, section MM), 1917
PMR (subsection, section MR), 1918
PNLT (subsection, section NLT), 1919
POD (section), 1920
polar decomposition
theorem PDM, 1921
polynomial
of a matrix
example PM, 1922
polynomial vector space
dimension
theorem DP, 1923
positive semi-definite
creating
theorem CPSM, 1924
positive semi-definite matrix
definition PSM, 1925
eigenvalues
theorem EPSM, 1926
practice
technique P, 1927
pre-image
definition PI, 1928
kernel
theorem KPI, 1929
pre-images
example SPIAS, 1930
principal axis theorem, 1931
product of triangular matrices
theorem PTMT, 1932
Property
AA, 1933
AAC, 1934
AACN, 1935
AAF, 1936
AAM, 1937
AC, 1938
ACC, 1939
ACCN, 1940
ACF, 1941
ACM, 1942
AI, 1943
AIC, 1944
AICN, 1945
AIF, 1946
AIM, 1947
C, 1948
CACN, 1949
CAF, 1950
CC, 1951
CM, 1952
CMCN, 1953
CMF, 1954
DCN, 1955
DF, 1956
DMAM, 1957
DSA, 1958
DSAC, 1959
DSAM, 1960
DVA, 1961
DVAC, 1962
MACN, 1963
MAF, 1964
MCCN, 1965
MCF, 1966
MICN, 1967
MIF, 1968
O, 1969
OC, 1970
OCN, 1971
OF, 1972
OM, 1973
SC, 1974
SCC, 1975
SCM, 1976
SMA, 1977
SMAC, 1978
SMAM, 1979
Z, 1980
ZC, 1981
ZCN, 1982
ZF, 1983
ZM, 1984
PSHS (example), 1985
PSHS (subsection, section LC), 1986
PSM (definition), 1987
PSM (section), 1988
PSM (subsection, section PSM), 1989
PSM (subsection, section SD), 1990
PSMSR (theorem), 1991
PSPHS (theorem), 1992
PSS (subsection, section SSLE), 1993
PSSD (theorem), 1994
PSSLS (theorem), 1995
PT (section), 1996
PTFP (example), 1997
PTM (example), 1998
PTMEE (example), 1999
PTMT (theorem), 2000
Q (archetype), 2001
R (acronyms, section JCF), 2002
R (archetype), 2003
R (chapter), 2004
range
full
example FRAN, 2005
isomorphic to column space
theorem RCSI, 2006
linear transformation
example RAO, 2007
notation, 2008
of a linear transformation
definition RLT, 2009
pre-image
theorem RPI, 2010
subspace
theorem RLTS, 2011
surjective linear transformation
theorem RSLT, 2012
via matrix representation
example RVMR, 2013
rank
computing
theorem CRN, 2014
linear transformation
definition ROLT, 2015
matrix
definition ROM, 2016
example RNM, 2017
notation, 2018, 2019
of transpose
example RRTI, 2020
square matrix
example RNSM, 2021
surjective linear transformation
theorem ROSLT, 2022
transpose
theorem RMRT, 2023
rank one decomposition
size 2
example ROD2, 2024
size 4
example ROD4, 2025
theorem ROD, 2026
rank+nullity
theorem RPNC, 2027
RAO (example), 2028
RCLS (theorem), 2029
RCSI (theorem), 2030
RD (subsection, section VS), 2031
RDS (theorem), 2032
READ (subsection, section B), 2033
READ (subsection, section CB), 2034
READ (subsection, section CRS), 2035
READ (subsection, section D), 2036
READ (subsection, section DM), 2037
READ (subsection, section EE), 2038
READ (subsection, section FS), 2039
READ (subsection, section HSE), 2040
READ (subsection, section ILT), 2041
READ (subsection, section IVLT), 2042
READ (subsection, section LC), 2043
READ (subsection, section LDS), 2044
READ (subsection, section LI), 2045
READ (subsection, section LISS), 2046
READ (subsection, section LT), 2047
READ (subsection, section MINM), 2048
READ (subsection, section MISLE), 2049
READ (subsection, section MM), 2050
READ (subsection, section MO), 2051
READ (subsection, section MR), 2052
READ (subsection, section NM), 2053
READ (subsection, section O), 2054
READ (subsection, section PD), 2055
READ (subsection, section PDM), 2056
READ (subsection, section PEE), 2057
READ (subsection, section RREF), 2058
READ (subsection, section S), 2059
READ (subsection, section SD), 2060
READ (subsection, section SLT), 2061
READ (subsection, section SS), 2062
READ (subsection, section SSLE), 2063
READ (subsection, section TSS), 2064
READ (subsection, section VO), 2065
READ (subsection, section VR), 2066
READ (subsection, section VS), 2067
READ (subsection, section WILA), 2068
reduced row-echelon form
analysis
notation, 2069
definition RREF, 2070
example NRREF, 2071
example RREF, 2072
extended
definition EEF, 2073
notation
example RREFN, 2074
unique
theorem RREFU, 2075
reducing a span
example RSC5, 2076
relation of linear dependence
definition RLD, 2077
definition RLDCV, 2078
REM (definition), 2079
REMEF (theorem), 2080
REMES (theorem), 2081
REMRS (theorem), 2082
RES (example), 2083
RGEN (theorem), 2084
RLD (definition), 2085
RLDCV (definition), 2086
RLT (definition), 2087
RLT (notation), 2088
RLT (subsection, section IS), 2089
RLT (subsection, section SLT), 2090
RLTS (theorem), 2091
RMRT (theorem), 2092
RNLT (subsection, section IVLT), 2093
RNM (example), 2094
RNM (subsection, section D), 2095
RNNM (subsection, section D), 2096
RNNM (theorem), 2097
RNSM (example), 2098
RO (definition), 2099
RO (notation), 2100
RO (subsection, section RREF), 2101
ROD (section), 2102
ROD (theorem), 2103
ROD2 (example), 2104
ROD4 (example), 2105
ROLT (definition), 2106
ROLT (notation), 2107
ROM (definition), 2108
ROM (notation), 2109
ROSLT (theorem), 2110
row operations
definition RO, 2111
elementary matrices, 2112, 2113
notation, 2114
row reduce
mathematica, 2115
ti83, 2116
ti86, 2117
row space
Archetype I
example RSAI, 2118
as column space, 2119
basis
example RSB, 2120
theorem BRS, 2121
matrix, 2122
notation, 2123
row-equivalent matrices
theorem REMRS, 2124
subspace
theorem RSMS, 2125
row-equivalent matrices
definition REM, 2126
example TREM, 2127
row space, 2128
row spaces
example RSREM, 2129
theorem REMES, 2130
row-reduce
the verb
definition RR, 2131
row-reduced matrices
theorem REMEF, 2132
RPI (theorem), 2133
RPNC (theorem), 2134
RPNDD (theorem), 2135
RR (definition), 2136
RR.MMA (computation, section MMA), 2137
RR.TI83 (computation, section TI83), 2138
RR.TI86 (computation, section TI86), 2139
RREF (definition), 2140
RREF (example), 2141
RREF (section), 2142
RREF (subsection, section RREF), 2143
RREFA (notation), 2144
RREFN (example), 2145
RREFU (theorem), 2146
RRTI (example), 2147
RS (example), 2148
RSAI (example), 2149
RSB (example), 2150
RSC5 (example), 2151
RSLT (theorem), 2152
RSM (definition), 2153
RSM (notation), 2154
RSM (subsection, section CRS), 2155
RSMS (theorem), 2156
RSNS (example), 2157
RSREM (example), 2158
RSSC4 (example), 2159
RT (subsection, section PD), 2160
RVMR (example), 2161
S (archetype), 2162
S (definition), 2163
S (example), 2164
S (section), 2165
SAA (example), 2166
SAB (example), 2167
SABMI (example), 2168
SAE (example), 2169
SAN (example), 2170
SAR (example), 2171
SAS (section), 2172
SAV (example), 2173
SC (definition), 2174
SC (example), 2175
SC (notation), 2176
SC (Property), 2177
SC (subsection, section S), 2178
SC (subsection, section SET), 2179
SC3 (example), 2180
SCAA (example), 2181
SCAB (example), 2182
SCAD (example), 2183
scalar closure
column vectors
Property SCC, 2184
matrices
Property SCM, 2185
vectors
Property SC, 2186
scalar multiple
matrix inverse, 2187
scalar multiplication
zero scalar
theorem ZSSM, 2188
zero vector
theorem ZVSM, 2189
zero vector result
theorem SMEZV, 2190
scalar multiplication associativity
column vectors
Property SMAC, 2191
matrices
Property SMAM, 2192
vectors
Property SMA, 2193
SCB (theorem), 2194
SCC (Property), 2195
SCM (Property), 2196
SD (section), 2197
SDS (example), 2198
SE (definition), 2199
SE (notation), 2200
secret sharing
6 ways
example SS6W, 2201
SEE (example), 2202
SEEF (example), 2203
SER (theorem), 2204
set
cardinality
definition C, 2205
example CS, 2206
notation, 2207
complement
definition SC, 2208
example SC, 2209
notation, 2210
definition SET, 2211
empty
definition ES, 2212
equality
definition SE, 2213
notation, 2214
intersection
definition SI, 2215
example SI, 2216
notation, 2217
membership
example SETM, 2218
notation, 2219
size, 2220
subset, 2221
union
definition SU, 2222
example SU, 2223
notation, 2224
SET (definition), 2225
SET (section), 2226
SETM (example), 2227
SETM (notation), 2228
shoes, 2229
SHS (subsection, section HSE), 2230
SI (definition), 2231
SI (example), 2232
SI (notation), 2233
SI (subsection, section IVLT), 2234
SIM (definition), 2235
similar matrices
equal eigenvalues
example EENS, 2236
eual eigenvalues
theorem SMEE, 2237
example SMS3, 2238
example SMS5, 2239
similarity
definition SIM, 2240
equivalence relation
theorem SER, 2241
singular matrix
Archetype A
example S, 2242
null space
example NSS, 2243
singular matrix, row-reduced
example SRR, 2244
singular value decomposition
theorem SVD, 2245
singular values
definition SV, 2246
SLE (acronyms, section NM), 2247
SLE (chapter), 2248
SLE (definition), 2249
SLE (subsection, section SSLE), 2250
SLELT (subsection, section IVLT), 2251
SLEMM (theorem), 2252
SLSLC (theorem), 2253
SLT (definition), 2254
SLT (section), 2255
SLTB (theorem), 2256
SLTD (subsection, section SLT), 2257
SLTD (theorem), 2258
SLTLT (theorem), 2259
SM (definition), 2260
SM (notation), 2261
SM (subsection, section SD), 2262
SM2Z7 (example), 2263
SM32 (example), 2264
SMA (Property), 2265
SMAC (Property), 2266
SMAM (Property), 2267
SMEE (theorem), 2268
SMEZV (theorem), 2269
SMLT (example), 2270
SMS (theorem), 2271
SMS3 (example), 2272
SMS5 (example), 2273
SMZD (theorem), 2274
SMZE (theorem), 2275
SNCM (theorem), 2276
SO (subsection, section SET), 2277
socks, 2278
SOL (subsection, section B), 2279
SOL (subsection, section CB), 2280
SOL (subsection, section CRS), 2281
SOL (subsection, section D), 2282
SOL (subsection, section DM), 2283
SOL (subsection, section EE), 2284
SOL (subsection, section F), 2285
SOL (subsection, section FS), 2286
SOL (subsection, section HSE), 2287
SOL (subsection, section ILT), 2288
SOL (subsection, section IVLT), 2289
SOL (subsection, section LC), 2290
SOL (subsection, section LDS), 2291
SOL (subsection, section LI), 2292
SOL (subsection, section LISS), 2293
SOL (subsection, section LT), 2294
SOL (subsection, section MINM), 2295
SOL (subsection, section MISLE), 2296
SOL (subsection, section MM), 2297
SOL (subsection, section MO), 2298
SOL (subsection, section MR), 2299
SOL (subsection, section NM), 2300
SOL (subsection, section O), 2301
SOL (subsection, section PD), 2302
SOL (subsection, section PDM), 2303
SOL (subsection, section PEE), 2304
SOL (subsection, section RREF), 2305
SOL (subsection, section S), 2306
SOL (subsection, section SD), 2307
SOL (subsection, section SLT), 2308
SOL (subsection, section SS), 2309
SOL (subsection, section SSLE), 2310
SOL (subsection, section T), 2311
SOL (subsection, section TSS), 2312
SOL (subsection, section VO), 2313
SOL (subsection, section VR), 2314
SOL (subsection, section VS), 2315
SOL (subsection, section WILA), 2316
solution set
Archetype A
example SAA, 2317
archetype E
example SAE, 2318
theorem PSPHS, 2319
solution sets
possibilities
theorem PSSLS, 2320
solution vector
definition SOLV, 2321
SOLV (definition), 2322
solving homogeneous system
Archetype A
example HISAA, 2323
Archetype B
example HUSAB, 2324
Archetype D
example HISAD, 2325
solving nonlinear equations
example STNE, 2326
SP4 (example), 2327
span
basic
example ABS, 2328
basis
theorem BS, 2329
definition SS, 2330
definition SSCV, 2331
improved
example IAS, 2332
notation, 2333
reducing
example RSSC4, 2334
reduction
example RS, 2335
removing vectors
example COV, 2336
reworking elements
example RES, 2337
set of polynomials
example SSP, 2338
subspace
theorem SSS, 2339
span of columns
Archetype A
example SCAA, 2340
Archetype B
example SCAB, 2341
Archetype D
example SCAD, 2342
spanning set
crazy vector space
example SSC, 2343
definition TSVS, 2344
matrices
example SSM22, 2345
more vectors
theorem SSLD, 2346
polynomials
example SSP4, 2347
SPIAS (example), 2348
SQM (definition), 2349
square root
eigenvalues, eigenspaces
theorem EESR, 2350
matrix
definition SRM, 2351
notation, 2352
positive semi-definite matrix
theorem PSMSR, 2353
unique
theorem USR, 2354
SR (section), 2355
SRM (definition), 2356
SRM (notation), 2357
SRM (subsection, section SR), 2358
SRR (example), 2359
SS (definition), 2360
SS (example), 2361
SS (section), 2362
SS (subsection, section LISS), 2363
SS (theorem), 2364
SS6W (example), 2365
SSC (example), 2366
SSCV (definition), 2367
SSET (definition), 2368
SSET (example), 2369
SSET (notation), 2370
SSLD (theorem), 2371
SSLE (section), 2372
SSM22 (example), 2373
SSNS (example), 2374
SSNS (subsection, section SS), 2375
SSNS (theorem), 2376
SSP (example), 2377
SSP4 (example), 2378
SSRLT (theorem), 2379
SSS (theorem), 2380
SSSLT (subsection, section SLT), 2381
SSV (notation), 2382
SSV (subsection, section SS), 2383
standard unit vector
notation, 2384
starting proofs
technique GS, 2385
STLT (example), 2386
STNE (example), 2387
SU (definition), 2388
SU (example), 2389
SU (notation), 2390
submatrix
notation, 2391
subset
definition SSET, 2392
notation, 2393
subspace
as null space
example RSNS, 2394
characterized
example ASC, 2395
definition S, 2396
in
example SP4, 2397
not, additive closure
example NSC2A, 2398
not, scalar closure
example NSC2S, 2399
not, zero vector
example NSC2Z, 2400
testing
theorem TSS, 2401
trivial
definition TS, 2402
verification
example SC3, 2403
example SM32, 2404
subspaces
equal dimension
theorem EDYES, 2405
surjective
Archetype N
example SAN, 2406
example SAR, 2407
not
example NSAQ, 2408
example NSAQR, 2409
not, Archetype O
example NSAO, 2410
not, by dimension
example NSDAT, 2411
polynomials to matrices
example SAV, 2412
surjective linear transformation
bases
theorem SLTB, 2413
surjective linear transformations
dimension
theorem SLTD, 2414
SUV (definition), 2415
SUV (notation), 2416
SUVB (theorem), 2417
SUVOS (example), 2418
SV (definition), 2419
SVD (section), 2420
SVD (subsection, section SVD), 2421
SVD (theorem), 2422
SVP4 (example), 2423
SYM (definition), 2424
SYM (example), 2425
symmetric matrices
theorem SMS, 2426
symmetric matrix
example SYM, 2427
system of equations
vector equality
example VESE, 2428
system of linear equations
definition SLE, 2429
T (archetype), 2430
T (definition), 2431
T (notation), 2432
T (part), 2433
T (section), 2434
T (technique, section PT), 2435
TCSD (example), 2436
TD (section), 2437
TD (subsection, section TD), 2438
TD (theorem), 2439
TD4 (example), 2440
TDEE (theorem), 2441
TDEE6 (example), 2442
TDSSE (example), 2443
TDSSE (subsection, section TD), 2444
technique
C, 2445
CD, 2446
CP, 2447
CV, 2448
D, 2449
DC, 2450
E, 2451
GS, 2452
I, 2453
L, 2454
LC, 2455
ME, 2456
N, 2457
P, 2458
PI, 2459
T, 2460
U, 2461
theorem
AA, 2462
AIP, 2463
AISM, 2464
AIU, 2465
AMA, 2466
AMSM, 2467
BCS, 2468
BIS, 2469
BNS, 2470
BRS, 2471
BS, 2472
CB, 2473
CCM, 2474
CCRA, 2475
CCRM, 2476
CCT, 2477
CFDVS, 2478
CFNLT, 2479
CHT, 2480
CILTI, 2481
CINM, 2482
CIVLT, 2483
CLI, 2484
CLTLT, 2485
CMVEI, 2486
CNMB, 2487
COB, 2488
CPSM, 2489
CRMA, 2490
CRMSM, 2491
CRN, 2492
CRSM, 2493
CRVA, 2494
CSCS, 2495
CSLTS, 2496
CSMS, 2497
CSNM, 2498
CSRN, 2499
CSRST, 2500
CSS, 2501
CUMOS, 2502
DC, 2503
DCM, 2504
DCP, 2505
DEC, 2506
DED, 2507
DEM, 2508
DEMMM, 2509
DER, 2510
DERC, 2511
DFS, 2512
DGES, 2513
DIM, 2514
DLDS, 2515
DM, 2516
DMFE, 2517
DMHP, 2518
DMMP, 2519
DMST, 2520
DNLT, 2521
DP, 2522
DRCM, 2523
DRCMA, 2524
DRCS, 2525
DRMM, 2526
DSD, 2527
DSFB, 2528
DSFOS, 2529
DSLI, 2530
DSZI, 2531
DSZV, 2532
DT, 2533
DVM, 2534
DZRC, 2535
EDELI, 2536
EDYES, 2537
EEMAP, 2538
EER, 2539
EESR, 2540
EIM, 2541
EIS, 2542
ELIS, 2543
EMDRO, 2544
EMHE, 2545
EMMVP, 2546
EMN, 2547
EMNS, 2548
EMP, 2549
EMRCP, 2550
EMS, 2551
ENLT, 2552
EOMP, 2553
EOPSS, 2554
EPM, 2555
EPSM, 2556
ERMCP, 2557
ESMM, 2558
ETM, 2559
FIMP, 2560
FS, 2561
FTMR, 2562
FVCS, 2563
G, 2564
GEK, 2565
GESD, 2566
GESIS, 2567
GSP, 2568
HMIP, 2569
HMOE, 2570
HMRE, 2571
HMVEI, 2572
HPC, 2573
HPDAA, 2574
HPHI, 2575
HPHID, 2576
HPSMM, 2577
HSC, 2578
ICBM, 2579
ICLT, 2580
IFDVS, 2581
IILT, 2582
ILTB, 2583
ILTD, 2584
ILTIS, 2585
ILTLI, 2586
ILTLT, 2587
IMILT, 2588
IMR, 2589
IP, 2590
IPAC, 2591
IPN, 2592
IPSM, 2593
IPVA, 2594
ISRN, 2595
ITMT, 2596
IVSED, 2597
JCFLT, 2598
KILT, 2599
KLTS, 2600
KNSI, 2601
KPI, 2602
KPIS, 2603
KPLT, 2604
KPNLT, 2605
LIVHS, 2606
LIVRN, 2607
LNSMS, 2608
LSMR, 2609
LTDB, 2610
LTLC, 2611
LTTZZ, 2612
MBLT, 2613
MCT, 2614
ME, 2615
MIMI, 2616
MISM, 2617
MIT, 2618
MIU, 2619
MLTCV, 2620
MLTLT, 2621
MMA, 2622
MMAD, 2623
MMCC, 2624
MMDAA, 2625
MMIM, 2626
MMIP, 2627
MMSMM, 2628
MMT, 2629
MMZM, 2630
MNEM, 2631
MRCB, 2632
MRCLT, 2633
MRMLT, 2634
MRRGE, 2635
MRSLT, 2636
MVSLD, 2637
NEM, 2638
NI, 2639
NJB, 2640
NME1, 2641
NME2, 2642
NME3, 2643
NME4, 2644
NME5, 2645
NME6, 2646
NME7, 2647
NME8, 2648
NME9, 2649
NMLIC, 2650
NMPEM, 2651
NMRRI, 2652
NMTNS, 2653
NMUS, 2654
NOILT, 2655
NPNT, 2656
NSMS, 2657
NVM, 2658
OBNM, 2659
OBUTR, 2660
OD, 2661
OSIS, 2662
OSLI, 2663
PCNA, 2664
PDM, 2665
PEEF, 2666
PIP, 2667
PSMSR, 2668
PSPHS, 2669
PSSD, 2670
PSSLS, 2671
PTMT, 2672
RCLS, 2673
RCSI, 2674
RDS, 2675
REMEF, 2676
REMES, 2677
REMRS, 2678
RGEN, 2679
RLTS, 2680
RMRT, 2681
RNNM, 2682
ROD, 2683
ROSLT, 2684
RPI, 2685
RPNC, 2686
RPNDD, 2687
RREFU, 2688
RSLT, 2689
RSMS, 2690
SCB, 2691
SER, 2692
SLEMM, 2693
SLSLC, 2694
SLTB, 2695
SLTD, 2696
SLTLT, 2697
SMEE, 2698
SMEZV, 2699
SMS, 2700
SMZD, 2701
SMZE, 2702
SNCM, 2703
SS, 2704
SSLD, 2705
SSNS, 2706
SSRLT, 2707
SSS, 2708
SUVB, 2709
SVD, 2710
TD, 2711
TDEE, 2712
technique T, 2713
TIST, 2714
TL, 2715
TMA, 2716
TMSM, 2717
TSE, 2718
TSRM, 2719
TSS, 2720
TT, 2721
TTMI, 2722
UMCOB, 2723
UMI, 2724
UMPIP, 2725
USR, 2726
UTMR, 2727
VFSLS, 2728
VRI, 2729
VRILT, 2730
VRLT, 2731
VRRB, 2732
VRS, 2733
VSLT, 2734
VSPCV, 2735
VSPM, 2736
ZSSM, 2737
ZVSM, 2738
ZVU, 2739
ti83
matrix entry (computation), 2740
row reduce (computation), 2741
vector linear combinations (computation), 2742
TI83 (section), 2743
ti86
matrix entry (computation), 2744
row reduce (computation), 2745
transpose of a matrix (computation), 2746
vector linear combinations (computation), 2747
TI86 (section), 2748
TIS (example), 2749
TIST (theorem), 2750
TIVS (example), 2751
TKAP (example), 2752
TL (theorem), 2753
TLC (example), 2754
TM (definition), 2755
TM (example), 2756
TM (notation), 2757
TM (subsection, section OD), 2758
TM.MMA (computation, section MMA), 2759
TM.TI86 (computation, section TI86), 2760
TMA (theorem), 2761
TMP (example), 2762
TMSM (theorem), 2763
TOV (example), 2764
trace
definition T, 2765
linearity
theorem TL, 2766
matrix multiplication
theorem TSRM, 2767
notation, 2768
similarity
theorem TIST, 2769
sum of eigenvalues
theorem TSE, 2770
trail mix
example TMP, 2771
transpose
matrix scalar multiplication
theorem TMSM, 2772
example TM, 2773
matrix addition
theorem TMA, 2774
matrix inverse, 2775, 2776
notation, 2777
scalar multiplication, 2778
transpose of a matrix
mathematica, 2779
ti86, 2780
transpose of a transpose
theorem TT, 2781
TREM (example), 2782
triangular decomposition
entry by entry, size 6
example TDEE6, 2783
entry by entry
theorem TDEE, 2784
size 4
example TD4, 2785
solving systems of equations
example TDSSE, 2786
theorem TD, 2787
triangular matrix
inverse
theorem ITMT, 2788
trivial solution
system of equations
definition TSHSE, 2789
TS (definition), 2790
TS (subsection, section S), 2791
TSE (theorem), 2792
TSHSE (definition), 2793
TSM (subsection, section MO), 2794
TSRM (theorem), 2795
TSS (section), 2796
TSS (subsection, section S), 2797
TSS (theorem), 2798
TSVS (definition), 2799
TT (theorem), 2800
TTMI (theorem), 2801
TTS (example), 2802
typical systems,
example TTS, 2803
U (archetype), 2804
U (technique, section PT), 2805
UM (definition), 2806
UM (subsection, section MINM), 2807
UM3 (example), 2808
UMCOB (theorem), 2809
UMI (theorem), 2810
UMPIP (theorem), 2811
unique solution,
example US, 2812
example USR, 2813
uniqueness
technique U, 2814
unit vectors
basis
theorem SUVB, 2815
definition SUV, 2816
orthogonal
example SUVOS, 2817
unitary
permutation matrix
example UPM, 2818
size 3
example UM3, 2819
unitary matrices
columns
theorem CUMOS, 2820
unitary matrix
inner product
theorem UMPIP, 2821
UPM (example), 2822
upper triangular matrix
definition UTM, 2823
US (example), 2824
USR (example), 2825
USR (theorem), 2826
UTM (definition), 2827
UTMR (subsection, section OD), 2828
UTMR (theorem), 2829
V (acronyms, section O), 2830
V (archetype), 2831
V (chapter), 2832
VA (example), 2833
Vandermonde matrix
definition VM, 2834
vandermonde matrix
determinant
theorem DVM, 2835
nonsingular
theorem NVM, 2836
size 4
example VM4, 2837
VEASM (subsection, section VO), 2838
vector
addition
definition CVA, 2839
column
definition CV, 2840
equality
definition CVE, 2841
notation, 2842
inner product
definition IP, 2843
norm
definition NV, 2844
notation, 2845
of constants
definition VOC, 2846
product with matrix, 2847, 2848
scalar multiplication
definition CVSM, 2849
vector addition
example VA, 2850
vector component
notation, 2851
vector form of solutions
Archetype D
example VFSAD, 2852
Archetype I
example VFSAI, 2853
Archetype L
example VFSAL, 2854
example VFS, 2855
mathematica, 2856
theorem VFSLS, 2857
vector linear combinations
mathematica, 2858
ti83, 2859
ti86, 2860
vector representation
example AVR, 2861
example VRC4, 2862
injective
theorem VRI, 2863
invertible
theorem VRILT, 2864
linear transformation
definition VR, 2865
notation, 2866
theorem VRLT, 2867
surjective
theorem VRS, 2868
theorem VRRB, 2869
vector representations
polynomials
example VRP2, 2870
vector scalar multiplication
example CVSM, 2871
vector space
characterization
theorem CFDVS, 2872
column vectors
definition VSCV, 2873
definition VS, 2874
infinite dimension
example VSPUD, 2875
linear transformations
theorem VSLT, 2876
over integers mod 5
example VSIM5, 2877
vector space of column vectors
notation, 2878
vector space of functions
example VSF, 2879
vector space of infinite sequences
example VSIS, 2880
vector space of matrices
definition VSM, 2881
example VSM, 2882
notation, 2883
vector space of polynomials
example VSP, 2884
vector space properties
column vectors
theorem VSPCV, 2885
matrices
theorem VSPM, 2886
vector space, crazy
example CVS, 2887
vector space, singleton
example VSS, 2888
vector spaces
isomorphic
definition IVS, 2889
theorem IFDVS, 2890
VESE (example), 2891
VFS (example), 2892
VFSAD (example), 2893
VFSAI (example), 2894
VFSAL (example), 2895
VFSLS (theorem), 2896
VFSS (subsection, section LC), 2897
VFSS.MMA (computation, section MMA), 2898
VLC.MMA (computation, section MMA), 2899
VLC.TI83 (computation, section TI83), 2900
VLC.TI86 (computation, section TI86), 2901
VM (definition), 2902
VM (section), 2903
VM4 (example), 2904
VO (section), 2905
VOC (definition), 2906
VR (definition), 2907
VR (notation), 2908
VR (section), 2909
VR (subsection, section LISS), 2910
VRC4 (example), 2911
VRI (theorem), 2912
VRILT (theorem), 2913
VRLT (theorem), 2914
VRP2 (example), 2915
VRRB (theorem), 2916
VRS (theorem), 2917
VS (acronyms, section PD), 2918
VS (chapter), 2919
VS (definition), 2920
VS (section), 2921
VS (subsection, section VS), 2922
VSCV (definition), 2923
VSCV (example), 2924
VSCV (notation), 2925
VSF (example), 2926
VSIM5 (example), 2927
VSIS (example), 2928
VSLT (theorem), 2929
VSM (definition), 2930
VSM (example), 2931
VSM (notation), 2932
VSP (example), 2933
VSP (subsection, section MO), 2934
VSP (subsection, section VO), 2935
VSP (subsection, section VS), 2936
VSPCV (theorem), 2937
VSPM (theorem), 2938
VSPUD (example), 2939
VSS (example), 2940
W (archetype), 2941
WILA (section), 2942
X (archetype), 2943
Z (Property), 2944
ZC (Property), 2945
ZCN (Property), 2946
ZCV (definition), 2947
ZCV (notation), 2948
zero
complex numbers
Property ZCN, 2949
field
Property ZF, 2950
zero column vector
definition ZCV, 2951
notation, 2952
zero matrix
notation, 2953
zero vector
column vectors
Property ZC, 2954
matrices
Property ZM, 2955
unique
theorem ZVU, 2956
vectors
Property Z, 2957
ZF (Property), 2958
ZM (definition), 2959
ZM (notation), 2960
ZM (Property), 2961
ZNDAB (example), 2962
ZSSM (theorem), 2963
ZVSM (theorem), 2964
ZVU (theorem), 2965