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| Ïîèñê ïî óêàçàòåëÿì |
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| Mehta M.L. — Matrix theory |
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| Ïðåäìåòíûé óêàçàòåëü |
Alexander matrix 305 308—311 354—355
Alexander matrix, polynomial 306 307 309 311 355
Alexandrof — Fenchel theorem 288
Alternant 101
Alternant as a Tdet 154—160
Alternant, confluent 102
Alternant, double 103 316—318
Arithmetic-harmonic mean inequality 212 341—342
Bezoutian 117 120—121
Binet — Cauchy formula 31
Binet — Cauchy formula for permanents 33
Birkoff's theorem 286
Cayley — Hamilton theorem 65
Characteristic equation 42 65—66
Conjectures 130 131 182 190 194 209
Convexity of matrix functions 121—126
Crossing number 303
Dependence, functional 113
Dependence, linear 25
Determinant 13—21 195—198 258
Determinant as a scalar product 20
Determinant of a direct product 21
Determinant of a quaternion matrix 139—143
Determinant of a sum of Hermitian matrices 169—174
Determinant of Schur product 186
Determinant with elements as Bernoulli or Euler numbers 319—323
Determinant, an integral of a 152—153
Determinant, Cauchy expansion of 17
Determinant, derivative of 19
Determinant, expansion by diagonal elements 19
Determinant, integral of a 152
Determinant, Laplace expansion of 17
Determinant, properties of 14—16
Diagonalization of normal matrices 46—48
Diagonalization of quaternion matrices 150
Direct powers of given symmetry 10
Direct product 9
Direct sum 3
Discrete Fourier Transform 127—133 326
Discriminant 117—119
Domain of values 237—243
Dual of a quaternion 137
Eigenvalues of direct powers of given symmetry 63—64
Eigenvalues of direct sum, product 63
Eigenvalues of Hermitian matrix and its sub-matrices 175—179
Eigenvalues of Hermitian matrix and partial traces 175—176
Eigenvalues of idempotents and nilpotents 52
Eigenvalues of quaternion matrices 145
Eigenvalues of special matrices 46
Eigenvalues, location of 243—246
Eigenvectors 42—46
Eliminant 117
Equation, characteristic 42 65—66
Equations, non-homogeneous linear 30
Equations, solution of linear 24
Fdet 141 144
Fischer — Lieb inequality 199
Formal power series 263
Frobenius — Kronig lemma 286
Functions of a matrix 65—66
Gauss sum (quadratic) 127 324—325
Gersgorin discs 245
Girard — Newton — Waring formula 257 274
Gram's formula 33 147—149
Group, permutation 17
Group, reflection 121—126
Hadamard inequality 85 188—190
Hafnian 15 104 314
Hermitian matrices, diagonalization of 46—48
Hermitian matrices, eigenvalues of 46
Hermitian matrices, ordered 192—195
Hermitian matrices, product of 209—211
hessian 114
Holder's inequality 340
Idempotent decomposition 58
Idempotent, principal 57
Immanent 16—17 192—198 207 261—262
Immanent as a scalar product 342—344
INDEX 59
Inequalities 163—209 346—350
Integral of a determinant 152
Integration over matrices 275—283
Integration over matrices, one matrix case 276—278
Integration over matrices, two matrix case 278—282
Inverse, generalized 220—235
Inverse, minors of the 34
Inverse, Moore — Penrose 227—231
Involution 259
Jacobian 113
Knot, Knots 302—312 354—355
Knot, Knots, diagram of 304
Knot, Knots, prime 303 304 310—311 354
Kronecker powers of given symmetry 10
Kronecker product 9
Linear dependence 25
Link 303
Matrices, matrix, Alexander 305 308 312 354
Matrices, matrix, anti-Hermitian 7 46
Matrices, matrix, anti-symmetric 7 46
Matrices, matrix, Cartan 121—126
Matrices, matrix, circulant 104—107
Matrices, matrix, circular 8 90
Matrices, matrix, commuting 51
Matrices, matrix, complex symmetric 93—97
Matrices, matrix, compound 34—36
Matrices, matrix, Coxeter 121—126 322—324
Matrices, matrix, definition of 2
Matrices, matrix, diagonal 5
Matrices, matrix, domain of values of a 237—243
Matrices, matrix, doubly stochastic 285—294
Matrices, matrix, dual of a 138
Matrices, matrix, elementary divisors of a 306
Matrices, matrix, elementary polynomial divisors of 353
Matrices, matrix, elements of 2
Matrices, matrix, g-inverse of 220—235
Matrices, matrix, Hadamard 109—111 134
Matrices, matrix, Hermitian 6 46—48 146 192—195 209—211
Matrices, matrix, Hermitian conjugate of 6
Matrices, matrix, idempotent 55—56
Matrices, matrix, induced permanental 207—209
Matrices, matrix, infinite 296—302
Matrices, matrix, inverse of a 23 314—315
| Matrices, matrix, minimal 291—294
Matrices, matrix, moment 107
Matrices, matrix, nil-potent 55—56
Matrices, matrix, non-singular 23
Matrices, matrix, normal commuting 51
Matrices, matrix, normal, diagonalization 46—48
Matrices, matrix, orthogonal 8
Matrices, matrix, partitioning of 5
Matrices, matrix, Pauli 138—139
Matrices, matrix, permutation 9
Matrices, matrix, persymmetric 107
Matrices, matrix, projection 48
Matrices, matrix, pure imaginary 7
Matrices, matrix, quaternion 137—160
Matrices, matrix, real 7
Matrices, matrix, real anti-symmetric 49—50
Matrices, matrix, real symmetric 49
Matrices, matrix, rectangular 2
Matrices, matrix, scalar 5
Matrices, matrix, self-dual 146
Matrices, matrix, singular 23
Matrices, matrix, spectral representation of 48
Matrices, matrix, spectrum of 70
Matrices, matrix, spread of a 246—248
Matrices, matrix, square 2
Matrices, matrix, symmetric 6
Matrices, matrix, symplectic 139
Matrices, matrix, Toeplitz 111—112
Matrices, matrix, transform of a 44
Matrices, matrix, transpose of a 5
Matrices, matrix, triangular, reduction to 52
Matrices, matrix, Turanian 107 164
Matrices, matrix, unit 5
Matrices, matrix, unitary 8 45 46 91
Matrices, matrix, zero 3
Matrices, sub-matrix 5
Minimal matrices 291—294
Minimal matrices, polynomials 67—69
Minors of the inverse 34
Moore — Penrose inverse 227—231
Norm, Euclidean 6
Norm, Hermitian 7
Number field 1
Orthonormalization (Schmidt) 44—51 149
Partial fractions 71
Partitions 252
Peirles — Bogoliubov inequality 185 202
Permanent 14 16 20 188—195 202—207 258 285—294 344
Permanent and hafnian 16
Permanent as a scalar product 20
Permanent of a circulant 190—192
Permanent of doubly stochastic matrices 285—294
Permanent, bounds for 202—206 349—350
Permanent, definition 14
Permanent, derivative of a 20
Permanent, Hadamard inequality for 188—190
Permanent, Schwartz' inequality for 195
Permutation 9 13 17 20 142 143 253
Perron — Frobenius theorem 98—99
Pfaffian 15 104 302 330
Pfaffian, expansion by quasi-diagonal elements 19
Polar forms 90—92
Polynomial, Alexander 306 307 309 310 355
Polynomial, characteristic 65—66
Polynomial, interpolating 69—70
Polynomial, minimal 67—69
Polynomial, prime 14
Polynomials, orthogonal 108—109 159 277 281 319—323 336—339
Polynomials, skew-orthogonal 319—323
Positive definite matrices criteriae 80—82
Positive definite matrices, factorization into 334
Positive definite matrices, properties of 84—86 91 214—216
Power means, inequalities 212—214
Power sums 256—258
Pseudo-inverse of Drazin 235
Quasi-diagonalization 49—50
Quasi-norm 6
Quaternion matrices 137—162 327—328
Quaternions 137—138
Rank 25—30 36 38 58—59 222—224
Rank, definition 25
Rank, factorization 29
Rank, reductions 27—28
Rank, removal of factors 29
Rank, some results about 26—30
Recurrent series 265—267
Reflection groups, finite 121—123 125
Reflection groups, infinite 123—124 126
Reflection groups, irreducible, of a group 16—17
Reflection groups, spectral, of a matrix 48
S-functions 259—261 264
S-functions, generalization of 271
S-functions, orthogonality of 269—271
S-functions, skew- 262 264
Scalar part of a quaternion 137
Scalar product, Euclidean 6
Scalar product, Hermitian 7
Schur product 5 186—188
Schwartz' inequalities 195—199 340
Series expansions, some 268
Singular value decomposition 60—63
Singular values 60
Stieltjeslan inequalities 165—167
Sylvester's theorem 37—40 115—117
Symmetric functions 252—273
Symmetric functions, complete 255—256
Symmetric functions, elementary 43 253—254
Symmetric functions, forgotten 259
Symmetric functions, monomial 253
Tdet 141—144 154—160 328 330 331—336
Torsion numbers 302 307 310
Trace 43
Trace of exponentials 183—186
Trace of logarithms and powers 201—202
Trace of products of matrices 179—182
Ulin's variational method 167
Vector, column 2
Vector, quasi-null 93
Vector, row 2
wronskian 115
Wronskian inequalities 163
Young diagram 252
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