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| Авторизация |
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| Horn R.A. — Matrix Analysis |
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| Предметный указатель |
Hadamard, product 321 455 456 457 474 475
Hadamard, square root of a matrix 462
Hahn — Banach theorem 288
Half-spaces 534
Hankel matrix 27 202 393
Hausdorff moment sequence 393
Hermitian adjoint 6
Hermitian matrices, *congruent 223 224
Hermitian matrices, product of three 469
Hermitian matrices, product of two 172
Hermitian matrix 104 167 169 397
Hermitian matrix, analogous to real numbers 170
Hermitian matrix, characterizations 171
Hermitian matrix, partitioned 175
Hermitian matrix, product with positive definite matrix 465
Hermitian matrix, spectral theorem 171
Hermitian part 109 170 399
Hermitian property 260
Hessenberg matrix 28 157
hessian 167 392 459 534
Hilbert matrix 341 401
Hoelder’s inequality 276 536
Hoffman — Wielandt Theorem 368 419
Holladay — Varga theorem 520
Homogeneous 259 260 290
Hopf’s bound 501
Householder, method 78
Householder, transformation 74 77 78 117
Hyperbolic differential operator 239
Hyperplane 534
Idempotent 37 148 311
Identity, backward, matrix 28 207
Identity, Jacobi 21
Identity, matrix 6
Identity, Newton 44
Identity, parallelogram 263
Identity, polarization 263
Identity, Sylvester 22
Ill-conditioned 336
Imaginary axis 532
Imaginary part of a complex number 531
inclusion principle 189
Inclusion region 378
Indefinite matrix 397
Independent 3
Index, citation 553
Index, of an eigenvalue 131 139 148
Index, of nilpotence 37
Index, of primitivity 519
Indicator matrix 356
Induced matrix norm 292
Induced matrix norm by absolute vector norm 310
Induced matrix norm by monotone vector norm 310 365
Induced matrix norm characterization 302 307
Inequality, arithmetic-geometric mean 535
Inequality, between matrix norms 314
Inequality, between vector norms 279
Inequality, bilinear 473
Inequality, Cauchy — Schwarz 15 261 277 535 536
Inequality, determinant 351
Inequality, Fischer 478
Inequality, Greub and Rheinboldt 452
Inequality, Grunsky 202
Inequality, Hadamard 199 200 477 483
Inequality, Hadamard — Fischer 485
Inequality, Hoelder 276 535
Inequality, Kantorovich 444 451 452
Inequality, matrix norm 290 312
Inequality, Minkowski 265 536
Inequality, Minkowski’s determinant inequality 482
Inequality, numerical radius 331
Inequality, Oppenheim 480
Inequality, Ostrowski — Taussky 468 481
Inequality, positive definite function 400
Inequality, power for numerical radius 333 334
Inequality, rank 352
Inequality, Robertson 468
Inequality, square root continuity 411
Inequality, submultiplicative 290
Inequality, Szasz 479
Inequality, triangle 259 290
Inequality, unitarily invariant matrix norm 450
Inequality, unitarily invariant norms 447
Inequality, weighted arithmetic-geometric mean 535
Inequality, Wielandt 442 443
Inertia of a matrix 221
Infinite series of matrices 300
Inner product 410
Inner product, characterization of norm derived from 263
Inner product, definition 260
Inner product, Frobenius 332
Inner product, standard 14
Inner product, usual 14
Interior point 282
Interlacing eigenvalues theorem for bordered matrices 185
Interlacing inequalities 182 185 187 189 200 404 419
Interlacing property for singular values 419
Interlacing theorem 182
Interpolation 29
Invariant factors 154
Invariant subspace 51
Inverse 14
Inverse, Brauer’s condition 381
Inverse, Brualdi’s condition 389
Inverse, diagonal dominance 355
Inverse, errors in 335
Inverse, generalized 421
Inverse, irreducibly diagonally dominant 363
Inverse, Levy — Desplanques condition 302 349
Inverse, minors of 21
Inverse, Ostrowski’s condition 381
Inverse, partitioned matrix 18 472
Inverse, series for 301
Inverse, small rank adjustment 18
Inverse, strict diagonal dominance 302 349
Invertible 14
Irreducible matrix 361 362 493 506—515
Irreducible matrix, minimal polynomial criterion 515
Irreducible normal form 506
Irreducibly diagonally dominant 362
Isometry 68
Isometry for a vector norm 266
Isometry group 266 267
Isomorphism 4
Jacobi identity 21
Jacobi method 76
Jacobian matrix 218
Jordan block 121
Jordan canonical form 121 129
Jordan canonical form, real 152
Jordan canonical form, theorem 126
Jordan Matrix 121 129
Jordan normal form 121
Kakeya’s theorem 318
Kantorovich’s inequality 444 451 452
Kernel 456 462
Kojima’s bound on zeroes 319 364
Krein — Milman theorem 533 534
Kronecker product 474 475
Krylov sequence 164
Ky Fan see "Fan"
Lagrange equations 227
Lagrange interpolating polynomial 29 188 405
Lagrange interpolation 29
Lagrange interpolation formula 30
Lanczos tridiagonalization 164
Laplace equation 239
Laplace expansion 7
Least squares, approximation 429 431 515
Least squares, solution 421
| Left eigenvector 59 371 497 504
Left Perron vector 497
Levy — Desplanques condition for invertibility 302 349
Levy — Desplanques theorem 302 349
Limit of a sequence 270
Limit point 282
Line segment 289
Linear dependence 3
Linear independence 3 407
Linear transformation 5
Loop 358
LU factorization 158—165
Lub norm 294
Majorization 199 425 446
Majorization and unitarily invariant norms 447
Majorization, characterizations 197
Majorization, definition 192
Majorization, eigenvalues by diagonal entries 193 196
Majorization, product inequality 199
Majorization, spectrum of a sum 194
Markov chain 497
Mason and Carmichael’s bound on zeroes 317 318 364
Matrix functions, generalized 8
Matrix norm,  norm 291
Matrix norm,  norm 291
Matrix norm,  norm 292
Matrix norm, bound norm 294
Matrix norm, Euclidean norm 291
Matrix norm, Fan k norms 445
Matrix norm, Frobenius norm 291
Matrix norm, generalized 320—342 see
Matrix norm, Hilbert — Schmidt norm 291
Matrix norm, induced 307 365
Matrix norm, induced by a similarity 296
Matrix norm, induced by vector norm 292 294
Matrix norm, inequalities between 314
Matrix norm, inequality for 312
Matrix norm, Ky Fan k norms see "Fan k norms"
Matrix norm, lub norm 294
Matrix norm, maximum column sum norm 294
Matrix norm, maximum row sum norm 295
Matrix norm, minimal 306 307
Matrix norm, not convex set 312
Matrix norm, operator norm 294
Matrix norm, Schatten p norm 441
Matrix norm, Schur norm 291
Matrix norm, self-adjoint 309
Matrix norm, spectral norm 295 441
Matrix norm, trace norm 441
Matrix norm, unitarily invariant 292 296 308
Matrix, adjacency 168 523
Matrix, almost diagonalizable 89
Matrix, approximation problems 427
Matrix, backward identity 207
Matrix, block diagonal 24
Matrix, block triangular 25 90
Matrix, bordered 185
Matrix, change of basis 32
Matrix, circulant 26
Matrix, combinatorially symmetric 523
Matrix, commuting 135
Matrix, companion 147 149 316
Matrix, complex orthogonal 71 72
Matrix, complex symmetric 201
Matrix, compound 19
Matrix, convergent 137
Matrix, correlation 400
Matrix, covariance 219 239 392 424
Matrix, diagonal 23
Matrix, diagonalizable 46 139 145
Matrix, doubly stochastic 197 527—529
Matrix, equivalent 164
Matrix, essentially nonnegative 506
Matrix, essentially triangular 26
Matrix, exponential 300
Matrix, function of a 300
Matrix, Gram 407
Matrix, Hankel 27 202 393
Matrix, hermitian 109 167 169
Matrix, Hessen berg 28
Matrix, Hessian 392 459 534
Matrix, Hilbert 341 401
Matrix, identity 6
Matrix, indefinite 397
Matrix, indicator 356
Matrix, inertia of a 221
Matrix, infinite series 300
Matrix, irreducible 361 362
Matrix, Jacobian 218
Matrix, Jordan 121 129
Matrix, negative definite 397
Matrix, nilpotent 139
Matrix, nonderogatory 135
Matrix, normal 100
Matrix, normal skew-symmetric 217
Matrix, normal symmetric 207
Matrix, orthogonal 71 72
Matrix, orthogonally diagonalizable 211
Matrix, orthostochastic 197
Matrix, permutation 25
Matrix, polynomial in a 36
Matrix, rank one 61
Matrix, Real orthogonal 66 72 107
Matrix, real skew-symmetric 107
Matrix, real symmetric 107
Matrix, reducible 360
Matrix, scalar 23
Matrix, signature of a 221
Matrix, similarity 44
Matrix, skew-Hermitian 100 169
Matrix, skew-orthogonal 72
Matrix, skew-symmetric 109
Matrix, skew-symmetric normal 217
Matrix, square root of 54 405
Matrix, stochastic 526—529
Matrix, symmetric 167 201
Matrix, symmetric diagonalizable 211
Matrix, symmetric normal 207
Matrix, symmetric unitary 215
Matrix, Toeplitz 27 136 137 394 409 456 462
Matrix, triangular 24
Matrix, tridiagonal 28 174 395 409 506
Matrix, unitary 66 109
Matrix, unitary characterizations 67
Matrix, unitary symmetric 215
Matrix, Vandermonde 29
Matrix, weakly irreducible 383
Max-min theorem 179 493 496 504
Maximal element 384
Maximum, column sum matrix norm 294
Maximum, of a continuous function 541
Maximum, row sum matrix norm 295
McCoy’s theorem 94 97
Mercer’s theorem 456
Metric convex hull 289
Min-max theorem 179 493 496
Minimal matrix norm 306 307
Minimal polynomial 142 145
Minimal polynomial, algorithm to compute 144 148
Minimal polynomial, criterion for irreducibility 515
Minimal polynomial, definition 143
Minimal polynomial, diagonalization criterion 145
Minimal polynomial, of a direct sum 149
Minimally spectrally dominant 330
Minkowski determinant inequality 482
Minkowski inequality 265 536
Minor 17
Minor, principal 17 40 398
Minor, signed 17
Modified Gram — Schmidt process 116
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