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Mehta M.L. Ч Matrix theory
Mehta M.L. Ч Matrix theory



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Ќазвание: Matrix theory

јвтор: Mehta M.L.

язык: en

–убрика: ћатематика/

—ери€: —делано в холле

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 393

ƒобавлена в каталог: 17.03.2011

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Alexander matrix      305 308Ч311 354Ч355
Alexander matrix, polynomial      306 307 309 311 355
Alexandrof Ч Fenchel theorem      288
Alternant      101
Alternant as a Tdet      154Ч160
Alternant, confluent      102
Alternant, double      103 316Ч318
Arithmetic-harmonic mean inequality      212 341Ч342
Bezoutian      117 120Ч121
Binet Ч Cauchy formula      31
Binet Ч Cauchy formula for permanents      33
Birkoff's theorem      286
Cayley Ч Hamilton theorem      65
Characteristic equation      42 65Ч66
Conjectures      130 131 182 190 194 209
Convexity of matrix functions      121Ч126
Crossing number      303
Dependence, functional      113
Dependence, linear      25
Determinant      13Ч21 195Ч198 258
Determinant as a scalar product      20
Determinant of a direct product      21
Determinant of a quaternion matrix      139Ч143
Determinant of a sum of Hermitian matrices      169Ч174
Determinant of Schur product      186
Determinant with elements as Bernoulli or Euler numbers      319Ч323
Determinant, an integral of a      152Ч153
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      14Ч16
Diagonalization of normal matrices      46Ч48
Diagonalization of quaternion matrices      150
Direct powers of given symmetry      10
Direct product      9
Direct sum      3
Discrete Fourier Transform      127Ч133 326
Discriminant      117Ч119
Domain of values      237Ч243
Dual of a quaternion      137
Eigenvalues of direct powers of given symmetry      63Ч64
Eigenvalues of direct sum, product      63
Eigenvalues of Hermitian matrix and its sub-matrices      175Ч179
Eigenvalues of Hermitian matrix and partial traces      175Ч176
Eigenvalues of idempotents and nilpotents      52
Eigenvalues of quaternion matrices      145
Eigenvalues of special matrices      46
Eigenvalues, location of      243Ч246
Eigenvectors      42Ч46
Eliminant      117
Equation, characteristic      42 65Ч66
Equations, non-homogeneous linear      30
Equations, solution of linear      24
Fdet      141 144
Fischer Ч Lieb inequality      199
Formal power series      263
Frobenius Ч Kronig lemma      286
Functions of a matrix      65Ч66
Gauss sum (quadratic)      127 324Ч325
Gersgorin discs      245
Girard Ч Newton Ч Waring formula      257 274
Gram's formula      33 147Ч149
Group, permutation      17
Group, reflection      121Ч126
Hadamard inequality      85 188Ч190
Hafnian      15 104 314
Hermitian matrices, diagonalization of      46Ч48
Hermitian matrices, eigenvalues of      46
Hermitian matrices, ordered      192Ч195
Hermitian matrices, product of      209Ч211
hessian      114
Holder's inequality      340
Idempotent decomposition      58
Idempotent, principal      57
Immanent      16Ч17 192Ч198 207 261Ч262
Immanent as a scalar product      342Ч344
INDEX      59
Inequalities      163Ч209 346Ч350
Integral of a determinant      152
Integration over matrices      275Ч283
Integration over matrices, one matrix case      276Ч278
Integration over matrices, two matrix case      278Ч282
Inverse, generalized      220Ч235
Inverse, minors of the      34
Inverse, Moore Ч Penrose      227Ч231
Involution      259
Jacobian      113
Knot, Knots      302Ч312 354Ч355
Knot, Knots, diagram of      304
Knot, Knots, prime      303 304 310Ч311 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      121Ч126
Matrices, matrix, circulant      104Ч107
Matrices, matrix, circular      8 90
Matrices, matrix, commuting      51
Matrices, matrix, complex symmetric      93Ч97
Matrices, matrix, compound      34Ч36
Matrices, matrix, Coxeter      121Ч126 322Ч324
Matrices, matrix, definition of      2
Matrices, matrix, diagonal      5
Matrices, matrix, domain of values of a      237Ч243
Matrices, matrix, doubly stochastic      285Ч294
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      220Ч235
Matrices, matrix, Hadamard      109Ч111 134
Matrices, matrix, Hermitian      6 46Ч48 146 192Ч195 209Ч211
Matrices, matrix, Hermitian conjugate of      6
Matrices, matrix, idempotent      55Ч56
Matrices, matrix, induced permanental      207Ч209
Matrices, matrix, infinite      296Ч302
Matrices, matrix, inverse of a      23 314Ч315
Matrices, matrix, minimal      291Ч294
Matrices, matrix, moment      107
Matrices, matrix, nil-potent      55Ч56
Matrices, matrix, non-singular      23
Matrices, matrix, normal commuting      51
Matrices, matrix, normal, diagonalization      46Ч48
Matrices, matrix, orthogonal      8
Matrices, matrix, partitioning of      5
Matrices, matrix, Pauli      138Ч139
Matrices, matrix, permutation      9
Matrices, matrix, persymmetric      107
Matrices, matrix, projection      48
Matrices, matrix, pure imaginary      7
Matrices, matrix, quaternion      137Ч160
Matrices, matrix, real      7
Matrices, matrix, real anti-symmetric      49Ч50
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      246Ч248
Matrices, matrix, square      2
Matrices, matrix, symmetric      6
Matrices, matrix, symplectic      139
Matrices, matrix, Toeplitz      111Ч112
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      291Ч294
Minimal matrices, polynomials      67Ч69
Minors of the inverse      34
Moore Ч Penrose inverse      227Ч231
Norm, Euclidean      6
Norm, Hermitian      7
Number field      1
Orthonormalization (Schmidt)      44Ч51 149
Partial fractions      71
Partitions      252
Peirles Ч Bogoliubov inequality      185 202
Permanent      14 16 20 188Ч195 202Ч207 258 285Ч294 344
Permanent and hafnian      16
Permanent as a scalar product      20
Permanent of a circulant      190Ч192
Permanent of doubly stochastic matrices      285Ч294
Permanent, bounds for      202Ч206 349Ч350
Permanent, definition      14
Permanent, derivative of a      20
Permanent, Hadamard inequality for      188Ч190
Permanent, Schwartz' inequality for      195
Permutation      9 13 17 20 142 143 253
Perron Ч Frobenius theorem      98Ч99
Pfaffian      15 104 302 330
Pfaffian, expansion by quasi-diagonal elements      19
Polar forms      90Ч92
Polynomial, Alexander      306 307 309 310 355
Polynomial, characteristic      65Ч66
Polynomial, interpolating      69Ч70
Polynomial, minimal      67Ч69
Polynomial, prime      14
Polynomials, orthogonal      108Ч109 159 277 281 319Ч323 336Ч339
Polynomials, skew-orthogonal      319Ч323
Positive definite matrices criteriae      80Ч82
Positive definite matrices, factorization into      334
Positive definite matrices, properties of      84Ч86 91 214Ч216
Power means, inequalities      212Ч214
Power sums      256Ч258
Pseudo-inverse of Drazin      235
Quasi-diagonalization      49Ч50
Quasi-norm      6
Quaternion matrices      137Ч162 327Ч328
Quaternions      137Ч138
Rank      25Ч30 36 38 58Ч59 222Ч224
Rank, definition      25
Rank, factorization      29
Rank, reductions      27Ч28
Rank, removal of factors      29
Rank, some results about      26Ч30
Recurrent series      265Ч267
Reflection groups, finite      121Ч123 125
Reflection groups, infinite      123Ч124 126
Reflection groups, irreducible, of a group      16Ч17
Reflection groups, spectral, of a matrix      48
S-functions      259Ч261 264
S-functions, generalization of      271
S-functions, orthogonality of      269Ч271
S-functions, skew-      262 264
Scalar part of a quaternion      137
Scalar product, Euclidean      6
Scalar product, Hermitian      7
Schur product      5 186Ч188
Schwartz' inequalities      195Ч199 340
Series expansions, some      268
Singular value decomposition      60Ч63
Singular values      60
Stieltjeslan inequalities      165Ч167
Sylvester's theorem      37Ч40 115Ч117
Symmetric functions      252Ч273
Symmetric functions, complete      255Ч256
Symmetric functions, elementary      43 253Ч254
Symmetric functions, forgotten      259
Symmetric functions, monomial      253
Tdet      141Ч144 154Ч160 328 330 331Ч336
Torsion numbers      302 307 310
Trace      43
Trace of exponentials      183Ч186
Trace of logarithms and powers      201Ч202
Trace of products of matrices      179Ч182
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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