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Lutkepohl H. — Handbook of Matrices
Lutkepohl H. — Handbook of Matrices

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Название: Handbook of Matrices

Автор: Lutkepohl H.

Аннотация:

Matrices are used in many areas such as statistics, econometrics, mathematics, natural sciences and engineering. This handbook provides a collection of numerous results for easy reference in one source, together with a comprehensive dictionary of matrices and related terms. The book is structured and cross-referenced so that specific results and information are easy to locate. References for proofs and computational algorithms are provided.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 309

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_1$-norm, properties of      109
$l_2$-norm      103
$l_p$-norm      103
Absolute norm      102
Absolute value of a matrix      5 39 225
Addition of matrices      3 225
Adjoint of a matrix      6 27 225
Adjugate of a matrix      226
Aitken's integral      152
Annihilating polynomial of a matrix      214 226
Antimetric matrix      226
Arithmetic matrix      226
Asymptotically stable polynomial      212
Band matrix      227
Band matrix, block      227
Banded matrix      227
Bidiagonal matrix      227
Binary matrix      227
Binet — Cauchy formula      49
Binomial formula      37 38
Block matrix      2 229
Block matrix, band      227
Block matrix, circulant      228
Block matrix, companion      220 228
Block matrix, diagonal      229
Block matrix, Hankel      229
Block matrix, properties of      144
Block matrix, Toeplitz      229
Block matrix, triangular      230
Block matrix, tridiagonal      230
Bordered Gramian matrix      230
Bordered matrix      230
Brownian matrix      230
Canonical forms, Choleski decomposition      86
Canonical forms, congruent      85
Canonical forms, diagonal reduction      85
Canonical forms, echelon      88
Canonical forms, Gram — Schmidt triangular reduction      87 92
Canonical forms, Hermite      88 249
Canonical forms, Jordan      83 84 254
Canonical forms, polar decomposition      88
Canonical forms, rank factorization      88
Canonical forms, real Choleski decomposition      92
Canonical forms, real Jordan      89
Canonical forms, real Schur decomposition      92
Canonical forms, Schur decomposition      86
Canonical forms, singular value decomposition      85 91
Canonical forms, Smith      222
Canonical forms, spectral decomposition      85 90
Canonical forms, triangular factorization      87
Cauchy — Schwarz inequality      43 54 104 111
Cayley — Hamilton theorem      67 216
Centro-Hermitian matrix      231
Centro-symmetric matrix      231
Chain rule for derivatives      174 176 202 206
Characteristic determinant of a matrix      12 231
Characteristic equation of a matrix      12 231
Characteristic matrix      220 231
Characteristic polynomial of a matrix      12 63 214 231
Characteristic root      12 63 231
Characteristic root, generalized      245
Characteristic root, in the metric of another matrix      231
Characteristic value      12 63 231
Characteristic value, generalized      245
Characteristic value, in the metric of another matrix      64
Characteristic vector      13 64 232 271
Characteristic vector, in the metric of another matrix      64 232
Check matrix      232 265
Choleski decomposition      86 154
Choleski decomposition of a real matrix      92 155
Circulant matrix      113 232
Circulant matrix, block      228
Circulant matrix, properties of      113
Cofactor matrix      232
Cofactor of an element of a matrix      6 232
Cogredietit matrices      233
Column dimension of a matrix      1 233
Column rank of a matrix      12 233
Column regular matrix      233
Column stochastic matrix      233
Column vector      2 233
Column vectorization of a matrix      233
Column vectorization operator      95
Column-sum norm      103
Column-sum norm, properties of      110
Common divisor of polynomials      212
Common factor of polynomials      212
Common left divisor of polynomial matrices      219 234
Common left divisor of polynomial matrices, greatest      247
Common right divisor of polynomial matrices      219 234
Common right divisor of polynomial matrices, greatest      247
Commutation matrix      9 31 97 115 123 127 234
Commutation matrix, properties of      115
Commuting matrices      234
Companion matrix      213 234
Companion matrix, block      228
Compatible norms      101 235
Complex conjugate matrix      235
Complex matrix      1 235
Compound matrix      235
Condition number of a matrix      236
Conditional inverse matrix      236
Conformable matrices      236
Congruent canonical form of a matrix      85 137
Congruent matrices      236
Conjugate of a matrix      5 24 236
Conjugate transpose of a matrix      5 25 236
Conjunctive matrices      236
Controllability matrix      236
Convergent matrix      119 236 277
Convergent matrix, properties of      119
Convergent polynomial      211
Coprime polynomials      212
Cosine of a matrix      215 236
Courant — Fischer theorem      67 68 133 159
D-inverse      236
Decomposable matrix      237 270
Decomposition of orthogonal matrix      144
Defective matrix      237
Deficient matrix      237
Definite matrix      237
Degree of a polynomial      211
Degree of a polynomial matrix      217 237
Dependent vectors      237
Derivative matrix      237
Derivatives of Hadamard products      184 192 199
Derivatives of inverse matrix      198
Derivatives of Kronecker products      184 192 199
Derivatives of the determinant      181
Derivatives of the trace      177
Derived norm      237
Derogatory matrix      214 237
Determinant      6 47 238
Determinant, Binet — Cauchy formula for      49
Determinant, derivatives of      181
Determinant, inequalities      54
Determinant, Jacobian      173 204
Determinant, of duplication matrix terms      51 53
Determinant, of elimination matrix terms      52 53
Determinant, of partitioned matrix      49
Determinant, optimization of      56
Determinant, Vandermonde      49 283
Diagonal dominant matrix      238
Diagonal matrix      5 9 120 238
Diagonal matrix, block      229
Diagonal matrix, properties of      120
Diagonal of a matrix      238 259
Diagonal reduction of a matrix      60 85
Diagonal similar matrix      238
Diagonalizable matrix      216 238
Difference of matrices      3 15
Dimension of a matrix      1 239 264
Dimension of a matrix column      233
Dimension of a matrix row      272
Direct product      3 239 279
Direct sum      4 22 239
Divergent polynomial      211
Dividing polynomial      212
Divisibility of a polynomial matrix, left      256
Divisibility of a polynomial matrix, right      271
Divisor, greatest common left      247
Divisor, greatest common right      247
Divisor, of a polynomial      212
Divisor, of a polynomial matrix, left      256
Divisor, of a polynomial matrix, right      271
Dominating      239
Dominating nonnegative matrix      239
Dominating principal diagonal      239
Dominating, principal      2
Dominating, secondary      273
Doubly centered matrix      239
Doubly quasi-stochastic matrix      240
Doubly stochastic matrix      139 240
Drazin inverse      240
Duplication matrix      9 31 51 53 97 118 122 127 130 157 165 240
Duplication matrix, properties of      122 149
Dyadic product      241
Echelon form      88 241
Effective inverse matrix      241
Eigenvalue      12 63 64
Eigenvalue, algebraic multiplicity      226
Eigenvalue, generalized      245
Eigenvalue, geometric multiplicity      246
Eigenvalue, Hopf's theorem for      142
Eigenvalue, in the metric of another matrix      64 241
Eigenvalue, inclusion principle      73 135 160
Eigenvalue, inequalities      72 134 159
Eigenvalue, multiplicity of      262
Eigenvalue, of a Hermitian matrix      133
Eigenvalue, of a matrix      241
Eigenvalue, of a polynomial matrix      218 241
Eigenvalue, of a positive definite matrix      153
Eigenvalue, of a symmetric matrix      158
Eigenvalue, Poincare's separation theorem      74 136 161
Eigenvalue, simple      63 275
Eigenvalue, Weyl's theorem      75 136 162
Eigenvector      13 64 242 271
Eigenvector matrix      241 261
Eigenvector, generalized      245
Eigenvector, in the metric of another matrix      64 242
Eigenvector, left      256
Eigenvector, right      271
Elementary divisors of a polynomial matrix      220 242
Elementary matrix      242
Elementary operations      12
Elementary operations, for a matrix      242
Elementary operations, for a polynomial matrix      219 242
Elementary polynomial matrix      219 242
Elements of a matrix      1
Elementwise product      3 243
Elimination matrix      9 31 52 53 97 118 123 126 127 165 243
Elimination matrix, properties of      127
Entries of a matrix      1
EP-matrix      243
Equality of matrices      243
Equivalent matrices      243
Equivalent polynomial matrices      220 243
Ergodic matrix      243
Euclidean norm      103
Euclidean norm, properties of      109
Exchange matrix      243 270
Exponential function of a matrix      215 244
Exponential matrix      244
Factor of a polynomial      212
Fischer's inequality for determinants      54 147 152
Flip matrix      244 270
Fourier matrix      114 244
Frobenius inequality      61
Frobenius matrix      244
Frobenius norm      103
Function of a matrix      259
g-circulant matrix      245
G-inverse matrix      245
Generalized characteristic root      245
Generalized characteristic value      245
Generalized eigenvalue      245
Generalized eigenvector of a matrix      245
Generalized inverse of a matrix      7 32 245 269
Generalized inverse rule for derivatives      209
Generalized permutation matrix      140 245
Geometric matrix      246
Geometric multiplicity of an eigenvalue      246
Givens matrix      246
Gradient matrix      246
Gradient vector      171 174 247
Gram matrix      247
Gram — Schmidt triangular reduction of a matrix      87
Gram — Schmidt triangular reduction of a nortsirtgular matrix      87
Gram — Schmidt triangular reduction of a real matrix      92
Gram — Schmidt triangular reduction of a real nonsingular matrix      92
Gram — Schmidt triangular reduction of a real square matrix      92
Gram — Schmidt triangular reduction of a square matrix      87
Gramian matrix      247
Gramian matrix, bordered      230
Greatest common divisor of polynomials      212
Greatest common factor of polynomials      212
Greatest common left divisor of polynomial matrices      219 247
Greatest common right divisor of polynomial matrices      219 247
Group inverse of a matrix      247
Hadamard matrix      247
Hadamard product      3 20 248
Hadamard product, derivatives of      184 192 199
Hadamard's inequality      54
Half-vectorization of a matrix      8 96 248
Half-vectorization operator      96 248
Hamiltonian matrix      248
Hankel matrix      249 265
Hankel matrix, block      229
Harmonic matrix      249
Helmert matrix      249
Hermite canonical form      88 249
Hermitian adjoint of a matrix      5 250
Hermitian form      12 250
Hermitian form, negative definite      262
Hermitian form, negative semidefinite      262
Hermitian form, positive definite      267
Hermitian form, positive semidefinite      267
Hermitian matrix      10 131 250
Hermitian matrix, decomposition of      137
Hermitian matrix, eigenvalues of      133
Hermitian matrix, properties of      131
Hessenberg matrix      250 283
Hessenberg matrix, lower      258
Hessian matrix      172 175 250
Hessian matrix, of the log determinant      182
Hessian matrix, of the trace      179
Hilbert matrix      251
Hilbert — Schmidt norm      103
Hoelder's inequality      44 111
Hopf's theorem for eigenvalues      78 142
Householder transformation      132 168 251
Hurwitz matrix      214 251
Hurwitz theorem      217
Idempotent matrix      10 138 251
Idempotent matrix, properties of      138
Identity matrix      2 10 252
Imaginary matrix      252
Imprimitive matrix      252
Inclusion principle for eigenvalues      73 135 160
Indefinite matrix      252
1 2 3 4
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