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| Lipschutz Seymour — Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines) |
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| Ïðåäìåòíûé óêàçàòåëü |
 52—53 72
 142
 40—41 53—54
Absolute value 52
Adjoint operator 425—426 433—436
Adjoint operator, matrix representation 426
Adjoint, classical 253—254
Algebra of linear maps 322
Algebraic multiplicity 285
Algorithm, basis-finding 154
Algorithm, determinant 253
Algorithm, diagonalization under, congruence 102—104
Algorithm, diagonalization under, similarity 102 286
Algorithm, Elimination (Gaussian) 8 24—25 100 261
Algorithm, Euclidean 446
Algorithm, Gauss — Jordan 29
Algorithm, inverse matrix 100
Algorithm, orthogonal diagonalization 289
Alternating bilinear form 411
angle 45 206
Annihilators 399—400 403—404
Arbitrary permutations 249
Augmented matrix 78
A{V) 322
B(V) 409
Back-substitution 9
Basis, dual 398 400—403
Basis, general solution 19—20
Basis, orthogonal 208
Basis, second dual 399
Basis, usual 150
Basis, vector space 150 169—171
Basis-finding algorithm 154
Bessel inequality 212
Bijective mapping 314
Bilinear form 409 414—416
Bilinear form, alternating 411
Bilinear form, Bilinear form, polar form of 412
Bilinear form, matrix representation of 410
Bilinear form, rank of 411
Bilinear form, real symmetric 412—413
Bilinear form, symmetric 411—412
Block matrix 79—80 86
Block matrix, determinant of 256—257
Block matrix, diagonal 98 291
Block matrix, Jordan 374
Block matrix, square 98 123—124
Block matrix, triangular 98
Cancellation law 142
Canonical form 14 352
Canonical form, Jordan 373—374 381—385
Canonical form, rational 375—376 388—390
Canonical form, row 14 16 28—30
Cauchy — Schwarz inequality 45 58 205—206 218
Cayley Hamilton theorem 282 302—304 307
cells 79
Change of basis 159—162 187—191
Change-of-basis matrix 160 348 357—359
Change-of-variable matrix 105—106
Characteristic polynomial 281—284 349
Classical adjoint 253—254
Codomain 312
Coefficient 1
Coefficient matrix 17 78
Coefficient, Fourier 211
Cofactor 252
column 13 74
Column, operations 100—102
Column, rank 152
Column, space 146
Column, vector 40 75
Commuting matrices 90
Companion matrix 291 375
Complement, orthogonal 207—208 226
Complex, conjugate 51
Complex, inner product 216—218
Complex, matrix 96 121—122
Complex, n-space 52
Complex, numbers 51
Component 40 211
Composition of mappings 313
Congruent, diagonalization 102—103
Congruent, matrices 102 410
Congruent, symmetric matrices 102—103 124—125
Conjugate matrix 96
Conjugate, complex 51
Consistent systems 13
Convex set 342 407
Coordinate vector 157 186—187
coordinates 40 157—159
cosets 376
Cramer's rule 255 263—264 268
Cross product 49—50 65—67
CURVES 48
Cyclic subspaces 374—375 388—389
Degenerate linear equations 2 3
Degree of polynomial 446
Dependence, linear 147 166—169
Determinant 246
Determinant, block matrix 256—257
Determinant, computation of 253 260—262
Determinant, linear equations 254—255
Determinant, linear operators 349
Determinant, multiplinearity 257—258
Determinant, order 3 248
Determinant, order n 250
Determinant, properties 251—252
Determinant, volume 257
Diagonal (of a matrix) 90
Diagonal matrix 93—94
Diagonal matrix, block 98
Diagonalizable matrices 280 288—289 298—301
Diagonalization 349—350 360—363
Diagonalization algorithm 102—104 286—288
Dimension of solution spaces 19
Dimension of vector spaces 150—151
Dimension of vector spaces, subspaces 151 171—172
Direct sum 156 181—186
Direct sum, decomposition 371 379—380
Directed line segment 46
Distance 45
Domain 312
Dot product 43—46 52 56—57
Dual basis 398
Dual space 397
Echelon form 10—11 14 23—24
Echelon matrices 14
Eigenvalue 284—285 292—298 350
Eigenvalue, computing 286—287
Eigenvector 284—286 292—298 350
Eigenvector, computing 286—287
Elementary divisors 376
Elementary matrix 99 101 117—118
Elementary operations 7—8
Elementary operations, column 100—102
Elementary operations, row 14 98—100
Elimination algorithm 6
Elimination, Gaussian 8 24—26 100 261
Enenspace 284 350
Equal matrices 74
Equal vectors 40
Equations See Linear equations
Equivalence, matric 100 102
Equivalence, row 14 16
Equivalent systems 7—8
Euclidean algorithm 446
Euclidean space 203
Evaluation map 92
Factorization, LU 109—111 130—133
Factorization, polynomial 448
| Field 74
Finite dimension 150—151
Fourier coefficient 211
Free variable 3 10
Function, spaces 143
Function, square matrix 89—90
Functional, linear 397
F{X) 143
Gauss — Jordan algorithm 29
Gaussian elimination 8 24—26 100 261
General solution 1 7
Geometric multiplicity 285
Gram — Schmidt orthogonalization 213
Graph 4
Greatest common divisor 447
Hermitian form 413—414
Hermitian matrix 97
Hermitian quadratic form 414
Hilbert space 205
Homogeneous systems 18—20 32—34 399—400
Hyperplane 46 407
Identity mapping 314
Identity matrix 91
ijk notation 49
Im F 316
Im z 51
Image of linear mapping 316—318 328—331
Imaginary part 51
Inconsistent systems 13
Independence, linear 147—150
Infinite dimension 150
Infinity-norm 219
Injective mapping 314
Inner product 202 221—226
Inner product spaces 202—205
Inner product spaces, linear operators on 425
Inner product, complex 216—218
Inner product, usual 203 214—216 218
Invariance 370—371
Invariant subspaces 370—371 377—378
Inverse matrix 92
Inverse matrix, computing algorithm 100
Invertible matrices 92—93 115—117
Invertible matrices, linear substitutions 105
Invertible matrices, operators 323
Isomorphic vector spaces 316
Isomorphism 158—159 316 320
Jordan block 374
Jordan canonical form 373—374
Ker F 316
Kernel of a linear map 316—320 328—332
Kronecker delta 91
Laplace expansion 252
Law of inertia 102 413
Leading nonzero entry 13
Leading unknown 3
Length 44 203
Line 47
linear combination 19 41—42 145—147 149 165—166
Linear dependence 42—43 147—149 166—169
Linear equation 1
Linear equation, degenerate 2—3
Linear equation, one unknown 2
Linear equations (system) 1 21 152—153 319—320 323—324 399—400
Linear equations (system), consistent 13
Linear equations (system), echelon form 10 23—24
Linear equations (system), triangular form 9—10 23
Linear equations (system), two unknowns 4—6
Linear functional 397 426—427
Linear independence 43 147—149
Linear mapping 314—316 319 326—328
Linear mapping, image 316—319 328—331
Linear mapping, kernel 316—320 328—332
Linear mapping, matrix representation 351
Linear mapping, nullity 318—319
Linear mapping, rank 318—319
Linear mapping, transpose 400
Linear operator 322
Linear operator, adjoint 425
Linear operator, characteristic polynomial 349
Linear operator, determinant 349
Linear operator, inner product spaces 425
Linear operator, invertible 323
Linear operator, matrix representation 344
Linear operator, nilpotent 373
Linear span 145
Located vectors 46
LU factorization 109—111 130—133
Mappings (maps) 312—314 324—326
Mappings (maps), composition of 313
Mappings (maps), linear 314—316 326—328
Matrices 13—14 74—75
Matrices, augmented 78
Matrices, block 79—80 86
Matrices, change-of-basis 160 348 430
Matrices, change-of-variable 105—106
Matrices, coefficient 17 78
Matrices, companion 375
Matrices, complex 96—97
Matrices, diagonal 93—94
Matrices, diagonizable 280 298
Matrices, echelon 14
Matrices, equivalent 102
Matrices, invertible 92—93
Matrices, nonsingular 92—93
Matrices, normal 97
Matrices, similar 357—359
Matrices, square 89—90
Matrices, triangular 94
Matrix representation, adjoint operator 426
Matrix representation, bilinear form 410—411
Matrix representation, linear maps 344 351 363—365
Matrix representation, quadratic form 104
Matrix space 142
Minimum polynomial 289—291 301—303 351
Minkowski's inequality 45
Minor 252 255—256
Minor principle 256
Monic polynomial 282 446
Multilinearity 257—258
Multiplication of matrices 76—77
Multiplicity 285
Multiplicity, n-space 40
Nilpotent 373
Nondegenerate linear equations 3
Nonnegative semidefinite 413
Nonsingular linear maps 320
Nonsingular matrices 92- 93
Norm 44 57—59 203 219—220 238
Normal matrix 97
Normal operator 428 432
Normal vector 46
Normalizing 44
Normed vector spaces 219—221
Nullity 318—319
One-norm 219—220
One-to-one correspondence 314
One-to-one mapping 314
Onto mapping 314
Operations on linear maps 320—321
Operators See Linear operators
Orthogonal basis 209
Orthogonal complement 207—208 226
Orthogonal matrix 95 216 429—430
Orthogonal operator 427—429 431—432
Orthogonal projections 433
Orthogonal sets 208—209 212
Orthogonality 43 226—229 280
Orthogonalization (Gram — Schmidt) 213
Orthonormal basis 209
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