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| Авторизация |
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| Поиск по указателям |
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| Robinson D.J.S. — A Course in Linear Algebra with Applications |
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| Предметный указатель |
Addition of linear operators 205
Addition of matrices 7
Adjoint of a matrix 92
Algebra 208
Algebra of linear operators 205
Algebra of matrices 210
Angle between two vectors 216
Associative law 14 28 32 111
Augmented matrix 3
Back substitution 38 42
Basis of a vector space 133
Basis of a vector space, change of 188
Basis of a vector space, ordered 140
Bijective function 170
Bilinear form 365
Bilinear form, matrix representation of 366
Bilinear form, skew-symmetric 369 375
Bilinear form, symmetric 369
Block, Jordan 390
Cauchy — Schwartz inequality 216 237
Cayley — Hamilton theorem 386
Change of basis 188
Change of basis and linear transformation 192
Characteristic equation 291
Characteristic polynomial 290 294
Codomain 169
Coefficient matrix 3
Cofactor 75
Column echelon form 56
Column expansion 76
Column operation 55
Column space 147
Column vector 4
Commutative law 14 28 29 1
Companion matrix 307
Complex inner product space 241
Complex scalar product 229
Complex transpose 228
Composite of functions 171
Congruent matrices 368
Congruent matrices, eigenvalues of 373
conic 348
Consistent linear system 42
Coordinate vector 140
Cost matrix 17
Cramer's rule 97
Critical point 271 359
Crossover diagram 69
Determinant of a product 90
Determinant, definition of 73
Determinant, properties of 80
Diagonal matrix 5
Diagonalizable matrix 299
Differential equations 126
Differential equations, system of 322
DIMENSION 137
Dimension formulas 157 201 245
Direct sum of subspaces 160
Distance from plane 218
Distributive law 14 28 111
Domain of a function 169
Echelon form 42
Eigenspace 290
Eigenvalue 288 298
Eigenvalue of hermitian matrix 335
Eigenvector 287 297
Elementary column operation 55
Elementary matrix 53
Elementary row operation 47
Equations, linear 3 35
Equations, linear, homogeneous 44
Equivalent linear systems 40
Euclidean space 102 235
Even permutation 69
Expansion column 76
Expansion row 76
Factorization, QR- 260
Fibonacci sequence 314
Field axioms of a 29
Field of two elements 30
Filippov 381
Finitely generated 118
Function 169
Fundamental subspaces 147 248
Fundamental theorem of algebra 2
Gauss — Jordan elimination 43
Gaussian elimination 39
General solution 40
Gram — Schmidt process 256
Group general linear 32
Group of  matrices 32
Group, axioms for 32
Hermitian matrix 335
hessian 362
Homogeneous linear differential equation 127
Homogeneous linear system 44
Identity element 28 32
Identity function 170
Identity linear operator 180
Identity matrix 5
Image of a function 169
Image of a linear transformation 198
Inconsistent linear system 40
Indefinite quadratic form 354
Infinitely generated 119
Injective function 170
Inner product 232
Inner product space 234 241
Inner product, complex 241
Inner product, real 232
Inner product, standard 233
Intersection of subspaces 155
Intersection of subspaces, finding basis of 162
Inverse of a function 173
Inverse of a matrix 20 59
Inversion of natural order 69
Invertible function 173
Invertible matrix 20
Isomorphic algebras 210
Isomorphic vector spaces 204
Isomorphism 203 210
Jordan block 390
Jordan normal form 391
Jordan string 390
Kernel 198
Law of inertia 374
Laws of exponents 26
Laws of matrix algebra 14
Least squares solution 270
Least squares, method of 268
Least squares, method of, and QR-factorization 277
Least squares, method of, geometric interpretation of 279
Least squares, method of, in inner product spaces 282
Length of a vector 214
Line segment 103
linear combination 116
Linear dependence 121
Linear differential equation 127
Linear independence 122
Linear mapping 177
Linear operator 177
Linear recurrence 308
Linear system of differential equations 322
Linear system of equations 3 35
Linear system of recurrences 311
Linear transformation 177
Linear transformation matrix representation of 181
Linearly dependent 121
Linearly independent 122
Lower triangular 5
| Markov process 317
Markov process, regular 319
Mathematical induction 401
Matrices, addition of 7
Matrices, congruent 368
Matrices, equality of 2
Matrices, multiplication of 9
Matrices, scalar multiplication of 7
Matrices, similar 196
Matrix, definition of 1
Matrix, diagonal 5
Matrix, diagonalizable 299
Matrix, elementary 53
Matrix, hermitian 335
Matrix, identity 5
Matrix, indefinite 354
Matrix, invertible 20
Matrix, negative definite 354
Matrix, non-singular 20
Matrix, normal 343
Matrix, orthogonal 262
Matrix, partitioned 23
Matrix, permutation 71
Matrix, positive definite 354
Matrix, powers of 12
Matrix, scalar 5
Matrix, skew-Hermitian 345
Matrix, skew-symmetric 14 376
Matrix, square 4
Matrix, symmetric 14
Matrix, triangular 5
Matrix, triangularizable 303
Matrix, unitary 265
Maximum, local 359
Method of least squares 268
Minimum polynomial 383
Minimum, local 359
Minor 74
Monk polynomial 383
Multiplication of matrices 9
Negative definite matrix 354
Negative definite quadratic form 354
Negative of a matrix 7
Negative of a vector 111
Negative semidefinite 364
Non-singular 20
Norm 236 238
Normal form of a matrix 57 151
Normal matrix 343
Normal system 272
Normed linear space 238
Null space of a matrix 115
Odd permutation 69
One-one 170
One-one correspondence 170
Onto 170
Operation, column 55
Operation, row 47
Optimal least squares solution 280
Ordered basis 140
Orthogonal basis 253
Orthogonal complement 242
Orthogonal linear operator 267
Orthogonal matrix 262
Orthogonal set 251
Orthogonal vectors 216
Orthogonality in  225
Orthogonality in inner product spaces 234
Orthonormal basis 253
Orthonormal set 251
Parallelogram rule 105
Partitioned matrix 23
Permutation 67
Permutation, matrix 71
Pivot 42
Polynomial characteristic 290 294
Polynomial minimum 383
Positive definite matrix 354
Positive definite quadratic form 354
Positive semidefinite 364
Powers of a matrix 12
Powers of a matrix, negative 27
Principal axes 350
Principal diagonal 5
Product of determinants 90
Product of linear operators 206
Product of matrices 9
Projection of a vector on a line 217
Projection of a vector on a subspace 247
QR-factorization 260
Quadratic form 346
Quadratic form, indefinite 354
Quadratic form, negative definite 354
Quadratic form, positive definite 354
Quadric surface 351
Rank of a matrix 151
Real inner product space 232
Recurrence, linear 308
Recurrence, linear, system of 311
Reduced column echelon form 56
Reduced echelon form 43
Reduced row echelon form 51
Reflection 197
Regular Markov process 319
Right-handed system 223
Ring with identity 28
Ring with identity matrix over 30
Ring with identity of matrices 31
Rotation 178 184 191 264
Row echelon form 48
Row expansion 76
Row operation 47
Row space 147
Row vector 4
Row-times-column rule 9
Saddle point 359
Scalar matrix 5
Scalar multiple of a linear operator 205
Scalar multiple of a matrix 7
Scalar multiplication 7
Scalar product 213
Scalar projection 217
Schur's theorem 337
Sign of a permutation 71
Similar matrices 196
Singular matrix 20
Skew-Hermitian matrix 345
Skew-symmetric bilinear form 369 375
Skew-symmetric matrix 14 376
Solution space 115 324
Solution, general 40
Solution, non-trivial 44
Solution, trivial 44
Spectral theorem 339
Standard basis of 134
Standard basis of  138
String, Jordan 390
subspace 113
Subspace, fundamental 147 248
Subspace, generated by a subset 117
Subspace, improper 113
Subspace, spanned by a subset 117
Subspace, zero 113
Sum of subspaces 155
Sum of subspaces, finding a basis for 162
Surjective function 170
Sylvester's law of inertia 374
Symmetric bilinear form 369
Symmetric matrix 14
System of differential equations 322
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