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| Hoffman K., Kunze R. — Linear algebra |
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| Предметный указатель |
 29
 29
Adjoint of transformation 295
Adjoint, classical 148 159
Admissible subspace 232
Algebra 117
Algebra of formal power series 119
Algebra, self-adjoint 345
Algebraically closed field 138
Alternating n-linear function 144 169
Annihilator of subset 101
Annihilator of sum and intersection 106(Ex. 11)
Annihilator of vector (T-annihilator) 201 202 228
Approximation 283
Associativity 1
Associativity of matrix multiplication 19 90
Associativity of vector addition 28
Augmented matrix 14
Axiom of Choice 400
Basis 41
Basis, change of 92
Basis, dual 99 165
Basis, for module 164
Basis, ordered 50
Basis, orthonormal 281
Basis, standard basis of 41
Bessel's inequality 287
Bilinear form 166 320 359
Bilinear form, diagonalization of 370
Bilinear form, group preserving 379
Bilinear form, matrix of 362
Bilinear form, non-degenerate (non-singular) 365
Bilinear form, positive definite 368
Bilinear form, rank of 365
Bilinear form, signature of 372
Bilinear form, skew-symmetric 375
Bilinear form, symmetric 367
Cauchy — Schwarz inequality 278
Cayley transform 309 (Ex. 7)
Cayley — Hamilton theorem 194 237
Characteristic of a field 3
Characteristic polynomial 183
Characteristic space 182
Characteristic value 182 183
Characteristic vector 182
Classical adjoint 148 159
Coefficients of polynomial 120
Cof actor 158
Column equivalence 256
Column operations 26 256
Column rank 72 114
Commutative algebra 117
Commutative group 83
Commutative ring 140
Companion matrix 230
Complementary subspace 231
Complementary subspace, orthogonal 286
composition 390
Conductor 201 202 232
Congruence 139 393 396
conjugate 271
Conjugate, transpose 272
Conjugation 276 (Ex. 13)
Coordinate matrix 51
coordinates 50
Coset 177 396
Cramer's rule 161
Cyclic decomposition theorem 233
Cyclic subspace 227
Cyclic vector 227
Degree of multilinear form 166
Degree of polynomial 119
Dependence, linear 40 47
Derivative of polynomial 129 266
Determinant function 144
Determinant function, existence of 147
Determinant function, for linear transformations 172
Determinant function, uniqueness of 152
Determinant rank 163 (Ex. 9)
Diagonalizable operator 185
Diagonalizable part of linear operator 222
Diagonalizable, simultaneously 207
Diagonalizatio, unitary 317
Diagonalization 204 207 216
Diagonalization of Hermitian form 323
Diagonalization of normal matrix (operator) 317
Diagonalization of self-adjoint matrix (operator) 314
Diagonalization of symmetric bilinear form 370
Differential equations 223 (Ex. 14) 249
DIMENSION 44
Dimension, formula 46
Direct sum 210
Direct sum of matrices 214
Direct sum of operators 214
Direct sum, invariant 214
Disjoint subspaces See Independent subspaces
Distance 289 (Ex. 4)
Division with remainder 128
Dual basis 99 165
Dual module 165
Dual space 98
Eigenvalue See Characteristic value
Elementary column operation 26 256
Elementary Jordan matrix 245
Elementary matrix 20 253
Elementary row operation 6 252
Empty set 388
Entries of a matrix 6
Equivalence relation 393
Equivalent systems of equations 4
Euclidean space 277
Exterior (wedge) product 175 177
Factorization of polynomial 136
Factors, invariant 239 261
Field 2
Field, algebraically closed 138
Field, subfield 2
Finite-dimensional 41
Finitely generated module 165
Form, alternating 169
Form, bilinear 166 320 359
Form, Hermitian 323
Form, matrix of 322
Form, multilinear 166
Form, non-degenerate, 324 (Ex. 6)
Form, non-negative 325
Form, normal 257 261
Form, positive 325 328
Form, quadratic 273 368
Form, r-linear 166
Form, rational 238
Form, sesqai-linear 320
Formal power series 119
Free module 164
Function 389
Function, determinant 144
Function, identity 390
Function, inverse of 391
Function, invertible 390
Function, linear 67 97 291
Function, multilinear 166
Function, n-linear 142
Function, polynomial function 30
Function, range of 389
Function, restriction of 391
Fundamental theorem of algebra 138
Gram — Schmidt process 280 287
Grassman ring 180
Greatest common divisor 133
Group 82
| Group, commutative 83
Group, general linear 307
Group, Lorentz 382
Group, orthogonal 380
Group, preserving a form 379
Group, pseudo-orthogonal 381
Group, symmetric 153
Hermitian See Self-adjoint
Hermitian form 323
Homogeneous system of linear equations 4
Hyperspace 101 109
Ideal 131
Ideal, principal ideal 131
Idempotent transformation See Projection
Identity element 117 140
Identity function 390
Identity matrix 9
Identity, resolution of 337 344
Independence, linear 40 47
Independent linearly 40 47
Independent subspaces 209
Inner product 271
Inner product, matrix of 274
Inner product, quadratic form of 273
Inner product, space 277
Inner product, standard 271 272
Integers 2
Integers, positive 2
Interpolation 124
Intersection 388
Intersection of subspaces 36
Invariant direct sum 214
Invariant factors of a matrix 239 261
Invariant subset 392
Invariant subspace 199 206 314
inverse of function 391
Inverse of matrix 22 160
Inverse, left 22
Inverse, right 22
Inverse, two-sided 22
Invertible function 390
Invertible linear transformation 79
Invertible matrix 22 160
Irreducible polynomial 135
Isomorphism of inner product spaces 299
Isomorphism of vector spaces 84
Jordan form of matrix 247
Kronecker delta 9
Lagrange interpolation formula 124
Laplace expansions 179
Left inverse 22
Linear algebra 117
Linear combination of equations 4
Linear combination of vectors 31
Linear equations See System of linear equations
Linear functional 97
Linear transformation (operator) 67 76
Linear transformation (operator), adjoint of 295
Linear transformation (operator), cyclic decomposition of 233
Linear transformation (operator), determinant of 172
Linear transformation (operator), diagonalizable 185
Linear transformation (operator), diagonalizable part of 222
Linear transformation (operator), invertible 79
Linear transformation (operator), matrix in orthonormal basis 293
Linear transformation (operator), matrix of 87 88
Linear transformation (operator), minimal polynomial of 191
Linear transformation (operator), nilpotent 222
Linear transformation (operator), non-negative 329 341
Linear transformation (operator), non-singular 79
Linear transformation (operator), normal 312
Linear transformation (operator), nullity of 71
Linear transformation (operator), orthogonal 303
Linear transformation (operator), polar decomposition of 343
Linear transformation (operator), positive 329
Linear transformation (operator), product of 76
Linear transformation (operator), quotient 397
Linear transformation (operator), range of 71
Linear transformation (operator), rank of 71
Linear transformation (operator), self-adjoint 298 314
Linear transformation (operator), semi-simple 263
Linear transformation (operator), trace of 106 (Ex. 15)
Linear transformation (operator), transpose of 112
Linear transformation (operator), triangulable 202
Linear transformation (operator), unitary 302
Linearly dependent (independent) 40 47
Lorentz group 382
Lorentz transformation 311 (Ex. 15) 382
Matrix 6
Matrix, augmented 14
Matrix, classical adjoint of 148 159
Matrix, coefficient 6
Matrix, cofactors 158
Matrix, companion 230
Matrix, conjugate transpose 272
Matrix, coordinate 51
Matrix, elementary 20 253
Matrix, elementary, Jordan 245
Matrix, identity 9
Matrix, invariant factors of 239 261
Matrix, inverse of 22 160
Matrix, invertible 22 160
Matrix, Jordan form of 247.
Matrix, minimal polynomial of 191
Matrix, nilpotent 244
Matrix, normal 315
Matrix, of bilinear form 362
Matrix, of form 322
Matrix, of inner product 274
Matrix, of linear transformation 87 88
Matrix, orthogonal 162(Ex. 4) 380
Matrix, positive 329
Matrix, principal minors of 326
Matrix, product 17 90
Matrix, rank of 114
Matrix, rational form of 238
Matrix, row rank of 56 72 114
Matrix, row-reduced 9
Matrix, row-reduced echelon 11 56
Matrix, self-adjoint (Hermitian) 35 314
Matrix, similarity of 94
Matrix, skew-symmetric 162 (Ex. 3) 210
Matrix, symmetric 35 210
Matrix, trace of 98
Matrix, transpose of 114
Matrix, triangular 155 (Ex. 7)
Matrix, unitary 163 (Ex. 5) 303
Matrix, upper-triangular 27
Matrix, Vandermonde 125
Matrix, zero 12
Minimal polynomial 191
Module 164
Module, basis for 164
Module, dual 165
Module, finitely generated 165
Module, free 164
Module, rank of 165
Monic polynomial 120
Multilinear function (form) 166
Multilinear function (form), degree of 166
Multiplicity 130
n-linear function 142
n-linear function, alternating 144 169
n-tuple 29
Nilpotent matrix 244
Nilpotent operator 222
Non-degenerate bilinear form 365
Non-degenerate form 324 (Ex. 6)
Non-negative form 325
Non-negative operator 329 341
Non-singular form See Non-degenerate
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