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| Авторизация |
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| Bhatia R. — Matrix Analysis |
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| Предметный указатель |
 -norms 84 89
 -mcasure of nonnormality 246
 theorem 224
 -length of a path 175
-optimal matching distance 173
Absolute value of a matrix 296
Absolute value of a vector 30
Absolute value, perturbation of 296
Adjoint 4
Analytic continuation 134
Analytic functions in a half-plane 134
Ando's Concavity Theorem 273
Angle operator 221
Angles between subspaces 201
Annihilation operator 21
Antisymmetric tensor power 16
Antisymmetric tensor product 16
Araki — Licb — Thirring inequality 258
Arithmetic-geometric mean inequality 87 262 295
Aronszajn's Inequality 64
Averaging 40 117
Bauer — Fike theorem 233
Bernstein's theorem 148
Bilinear functional 12
Bilinear functional, elementary 12
Bilinear map 12 310 313
Binomial operator 284
Biorthogonal 2
Birkhoff's theorem 37 180
Block-matrix 9 195
Borel measure 139
Bound norm 7
C-numerical radius 102 106
Canonical angles 201
Caratheodory's theorem 38
Carrollian n-tuple 242
Cartesian decomposition 6 25 73 156 183
Cauchy — Riemann equations 135
Cauchy — Schwarz inequality for matrices 266 286 297 298
Cauchy — Schwarz inequality for symmetric gauge functions 88
Cauchy — Schwarz inequality for unitarily invariant norms 95 108
Cauchy's integral formula 205
Cauchy's Interlacing Theorem 59
Cayley transform 284
Centraliser 167
Chain rule 311
Chebyshev's theorem 228
Cholesky decomposition 5 319
Class  268
Class  259
Coefficients in the characteristic polynomial 269
Commutant 167
Commutator 167 234
Compatible matching 36
Complete symmetric polynomial 18
Completely monotone function 148
Compression 59 61 119
Concave function 41 53 158 240 248 289
Condition number 232
Conformally equivalent 137
Contraction 7 119
Contractive 7 10
Convex function 40 41 45 87 117 157 218 240 248 265 281
Convex function, monotone 40
Convex function, smoothness properties 145
Convolution 146
Cosines of 201
Creation operator 21
CS decomposition 196 223
Cyclic order 184 191
Davis — Kahan  Theorem 212
Derivative 124 310
Determinant 16 253 269
Determinant, inequality 3 19 21 47 51 108 181 182 183 271 281
Determinant, perturbation of 22
Diagonal of A 37
Diagonalisable matrix 232
Diagonally dominant 251
Differentiable curve 166
Differentiable manifold 305
Differentiable map 124 310
Differentiation, rules of 311
Dilation Theory 26
Direct sum 9
Directional derivative 310
Distance between subspaces 202
Distribution function 139
Doubly stochastic matrix 23 32 165
Doubly substochastic matrix 38 39
Dual norm 89 96
Dual space 14
Dyson's expansion 311 319
Eigenvalues 24 58 67 77
Eigenvalues of A with respect to B 238
Eigenvalues of Hermitian matrices 24 35 62 101
Eigenvalues of product of unitary matrices 82
Eigenvalues, continuity of 152 168
Eigenvalues, continuous parametrization of 154
Eigenvalues, generalised 238
Elementary symmetric polynomi¬als 18 46 51
entropy 44 274 287
Entropy in quantum mechanics 274
Entropy, relative 274
Euclidean norm 86
Exponential 8 254 311
Extremal representation for singular values 75 76
Fan Dominance Theorem 93 284 291
Fan — Hoffman theorem 73
Field of values 8
First divided difference 123
Fischer's inequality 51
Fourier analysis 135
Fourier transform 206 207 216
Fourier transform, inverse 216
Fourier transform, minimal extrapolation problem 224
Frechet derivative 310
Frechet differentiable map 124
Frechet differential calculus 301 310
Frobenius norm 7 25 92 214
Fubini's theorem 140
Fuglede — Putnam theorem 235
Function of bounded variation 217
G Marriage Theorem 162 213
Gamma function 319
Gap 225
Gel'fand Nainiark Theorem 71
General linear group 7
Gersgorin Disk Theorem 244
Gersgorin disks 244
Golden — Thompson inequality 261 279 285
Gram determinant 20
Gram matrix 20
Gram — Schmidt procedure 2 287
Grassmann power 18
Hadamard Determinant Theo¬rem 24 46 51
Hadamard product 23
Hadamard's inequality 3 227
Hall's Marriage Theorem 36
Hall's theorem 52
Harmonic conjugates 137
Harmonic function 135
Harmonic function, harmonic function, mean value property 136
Hausdorff distance 160
Heinz inequalities 285
Henrici's Theorem 246
Herglotz theorem 136
Hermitian approxirnant 276
Hermitian matrix 4 8 57 155 254
Hilbert — Schmidt norm 7 92 97 299
Hoelder inequality 88
| Hoelder inequality for symmetric gauge functions 88
Hoelder inequality for unitarily invariant norms 95
Hoffman — Wielandt inequality 165 237
Hoffman — Wielandt Theorem 165
Hyperbolic PDE 251
Hyperbolic polynomials 251
Imaginary part of a matrix 6
Inner product 1
Inner product, on matrices 92
Interlacing theorem 60
Interlacing theorem for singular values 81
Interlacing theorem, converse 61
Invariant subspace 10
Inverse 293
Isometry 119
Isotone 41
Jointly concave 271 273
Jordan canonical form 246
Jordan decomposition 99 262 277 292
Kato — Temple inequality 77
Koenig — Frobenius theorem 37
Krein — Milman theorem 133
Ky Fan k-norms 35 92
Ky Fan k-norms, main use 93
Ky Fan's Maximum Principle 24 35 65 69 71 174
Lattice superadditive 48 53
Laxly positive 238
Lebosguo Dominated Convergence Theorem 139
Length of a curve 169
Lexicographic ordering 14
Lidskii's theorem 69 179
Lidskii's Theorem for normal matrices 181
Lidskii's Theorem, multiplicative 73
Lidskii's Theorem, second proof 70
Lidskii's Theorem, third proof 98
Lie algebra 241
Lie bracket 167
Lie product formula 254 280
Lieb — Thirring inequality 279
Lieb's Concavity Theorem 271
Lieb's theorem 270
Liebian function 286
Lindblad's theorem 275
Lipschitz constant 215
Lipschitz continuous 322
Lipschitz continuous function 214
Loewdin orthogorialisation 287
Loewner — Heinz Theorem 285
Loewner's Theorems 131 149
Logarithm 145
Logarithm, principal branch 143
Logarithmic majorisation 71
Loowner — Heiuz inequality 150
LR decomposition 319
LR decomposition, pert urbation of 320
Lyapunov equation 221
Majorisation 28
Majorisation of complex vectors 179
Majorisation, soft 180
Majorisation, weak 30
Manifold 167
Marcus-de Oliviera Conjecture 184
Marriage problem 3
Matching problem 36
Matching theorem 185
Matrix convex 113
Matrix convex of order n 113
Matrix monotone 112
Matrix monotone of onlor 11 112
Matrix tiangle inequality 81
Matrix Young inequalities 286
Mean value theorem 303 307 312
Measure of nonnormality 245 251 278
Metrically flat 170
Mid-point operator confex 113
Minimax principle 58
Minimax principle for singular values 75
Minimax principle of Courant, Fischer and Weyl 58
Minkowski determinant inequality 56
Minkowski determinant theorem 47 282
Minkowski inequality, for symmetric gauge functions 89
Mirman's Theorem 25
Mixed Schwarz inequality 281 286
Mollifiers 146
Monotone 45 48
Monotone decreasing 41
Monotone increasing 41
Multi-indices 16
Multilinear functional 12
Multilinear map 12
Multiplication operator 223
Multiplication operator, left 273
Multiplication operator, right 273
Nearly normal matrix 252
Neumann series 7
Nevanlinna's theorem 138
Nevanlinna's Theorem, absolute 85
Nevanlinna's Theorem, bound 91
Nevanlinna's Theorem, Frobenius 92
Nevanlinna's Theorem, gauge invariant 85
Nevanlinna's Theorem, Hilbert-Schinidt 92
Nevanlinna's Theorem, Ky Fan 92
Nevanlinna's Theorem, monotone 85
Nevanlinna's Theorem, norm 1 6
Nevanlinna's Theorem, operator 91
Nevanlinna's Theorem, permutation invariant 85
Nevanlinna's Theorem, Schatten 92
Nevanlinna's Theorem, submultiplicative 94
Nevanlinna's Theorem, symmetric 85
Nevanlinna's Theorem, trace 92
Nevanlinna's Theorem, unitarily invariant 91
Nevanlinna's Theorem, weakly unitarily invariant 102
Normal approximant 277
Normal curve 169
Normal matrices, distance between eigenvalues 212
Normal matrices, path connected 169
Normal matrix 4 8 160 161 168 172 177 180 253
Normal matrix, function of 5
Normal matrix, spectral resolution 161
Normal path 169 177
Normal path inequality 189
Numerical radius 8 102
Numerical range 8 25
Operator approximation 192 275 287
Operator concave function 113 121
Operator convex function 113 130
Operator convex function, integral representation. 134
Operator monotone function 112 121 126 127 130 289 302 303 304 317
Operator monotone function, canonical representation 145
Operator monotone function, infinitely differentiable 134 290
Operator monotone function, integral representation 134
Operator monotone function, inverse of 293
Operator norm 7
Optimal matching 159
Optimal matching distance 52 153 160 21
Orbit 189
Orthostochastic matrix 35 180
P-Carrollian 242
p-norms 84
Partitioned matrix 64 188
Peierls — Bogoliubov inequality 275 281
Permanent 17 19
Permanent, inequality 19 21 23
Permanent, perturbation of 22
Permutation invariant 43
Permutation matrix 32 37 165
Permutation matrix, complex 85
Permutation orbit 166
permutations 165
Pick functions 135 139
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