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| Авторизация |
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| Поиск по указателям |
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| Bhatia R. — Matrix Analysis |
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| Предметный указатель |
Pick functions, integral representation 138
Pick functions, Nevanlinna's Theorem 135
Pinching 50 97 118 275
Pinching inequality 97
Pinching inequality for wul norms 107
Poincare's inequality 58
Poisson kernel 136
Polar decomposition 6 213 267 276 305
Polar decomposition, perturbation of 305
Positive approximant 27 7
Positive definite 4
Positive matrices, product of 255
Positive matrix 4
Positive part 6 213
Positive semidefinite 4
Positivity-preserving 32
Power functions 123 145 289
Power functions, operator convexity of 123
Power functions, operator monotonicity of 123
Power functions, principal branch 143
Principal angles 202
Probability measure 133
Probability measures, weak* compact 130
Product rule for differentiation 312
Pth derivative 315
Pythagorean Theorem 21
Q'-norm 90 97
Q-norm 89 95 174 175 277
QR decomposition 3 195 307
QR decomposition, perturbation of 307
QR decomposition, rank revealing 196
Quantum chemistry 287
Quasi-norms 107
R factor 195
Real eigenvalues 238
Real part of a matrix 6
Real spectrum 193
Rectifiable normal path 169
Rectifiable path 169
Reducing subspace 10
Regularisation 146
Residual bounds 193
Retraction 173 277
Roots of polynomials 230
Roots of polynomials, continuity of 154
Roots of polynomials, perturbation of 230
Rotfel'd's Theorem 98
Rouche's theorem 153
S-convex 40
Schatten 2-norm 7
Schatten class 321
Schatten p-norm 92 297 298
Schur basis 5
Schur product 23 124
Schur Triangular Form 5
Schur's theorem 23 35 47 51 74
Schur's Theorem, converse of 55
Schur-concave 44 46 53
Schur-convex 40 41 44
Schur-convexity, and convexity 46
Schur-convexity, for differentiable functions 45
Schwartz space 219
Second derivative 313
Second divided difference 128
Self-adjoint 4
Sesquilinear functional 12
Signature of a permutation 16
Similarity orbit 189
Similarity transformations 102
Singular value decomposition 6
Singular values 5
Singular values of products 71
Singular values, inequalities 94
Singular values, majorisation 157
Singular values, perturbation of 78
Singular vectors 6
Singular vectors, perturbation of 215
Skew-Hermitian 4 155
Skew-symmetric 241
Smooth approximate identities 146
| Spcctral resolution 57
Spectral radius 9 102 253 256 269
Spectral radius formula 204
Spectral theorem 5
Square root 297 301
Square root of a positive matrix 5
Square root, principal branch 143
Stieltjes inversion formula 139
Strictly isotone 41
Strictly positive 4
Strongly isotone 41
Strongly nonsingular 319
Subadditive 53
Subspaces 201
Sylvester equation 194 203 222 223 234
Sylvester equation, condition for a unique solution 203
Sylvester equation, norm of the solution 208
Sylvester equation, solution of 204 205 206 207 208
Symmetric gauge function 44 52 86 90 260
Symmetric gauge function, quadratic 89
Symmetric matrix 241
Symmetric norm 94
Symmetric tensor power 16 18
Symmetric tensor product 16
Symmetry classes of tensors 17
Symplectic, Lie algebra 241
Symplectic, Lie group 241
T-transform 33
Tan theorem 222
Tangent space 167 305
Tangent vector 166
Taylor's theorem 303 307 315
Tempered distribution 219
Tensor product 222
Tensor product of operators 14
Tensor product of spaces 13
Tensor product, construction 12
Tensor product, inner product on 14
Tensor product, orthonormal basis for 14
Toeplitz — Hausdorff theorem 8 20
Trace 25 253 269
Trace inequality 258 261 279 281
Trace norm 92 173
Trace of a vector 29
Trace-preserving 32
Triangle inequality for the matrix absolute value 74
Tridiagonal matrix 60
Twice differentiable map 313
Tychonoff's theorem 132
Unital 32
Unitarily equivalent 5
Unitarily invariant function norm 104
Unitarily invariant norm 91 93
Unitarily similar 5
Unitary approximant 276
Unitary conjugation 102 166
Unitary factors 307
Unitary group 7
Unitary invariance 7
Unitary matrix 4 162 178
Unitary orbit 166
Unitary part 6 82 213 305
Unitary-stochastic 35
Unordered n-tuples 153
Unordered n-tuples, metric on 153
Unordered n-tuples, quotient topology on 153
Van der Waerden conjecture 27
Variance 44
Weak submajorisation 30
Weakly unitarily invariant norm 102 109
Weyl's inequalities 62 64
Weyl's Majorant Theorem 42 73 254 279
Weyl's Majorant Theorem, converse of 55
Weyl's Monotonicity Principle 100 291 292
Weyl's Monotonidty Theorem 63
Weyl's Perturbation Theorem 63 71 99 152 240
Wielandt's Minimax Principle 67
Wigner — Yanase — Dyson conjecture 274
Wui norm 102 173 177 190
Wui seminorm 102
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