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| Авторизация |
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| Поиск по указателям |
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| Lutkepohl H. — Handbook of Matrices |
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| Предметный указатель |
Polynomials, greatest common divisor of 212
Polynomials, greatest common factor of 212
Polynomials, least common multiple of 212
Polynomials, relatively prime 212
Positive definite Hermitian form 267
Positive definite matrix 10 267
Positive definite matrix, properties of 150
Positive definite quadratic form 267
Positive matrix 11 139 267
Positive matrix, properties of 139
Positive semidefinite Hermitian form 267
Positive semidefinite matrix 10 267
Positive semidefinite matrix, properties of 150
Positive semidefinite quadratic form 267
Postmultiplication by a matrix 267
Power of a matrix 7 37 267
Power series, matrix 215
Premultiplication by a matrix 268
Primitive matrix 268
Principal diagonal of a matrix 2 268
Principal minor of a matrix 6 268
Principal submatrix 268
Principal vector of a matrix 269
Product matrix 269
Product rule for derivatives 174 176 189 208
Product, direct 3 239
Product, dyadic 241
Product, elementwise 3 243
Product, Hadamard 3 20 248
Product, Kronecker 3 19 256
Product, matrix 3 16 260 269
Product, scalar 273
Product, Schur 3 273
Product, tensor 3 279
Projection matrix 269
Projector, orthogonal 265
Pseudo-inverse matrix 269
Pythagoras theorem 104
Quadratic form 12 269
Quadratic form, negative definite 262
Quadratic form, negative semidefinite 263
Quadratic form, positive definite 267
Quadratic form, positive semidefinite 267
Quadratic matrix 2 269 276
Quotient of polynomial matrices, left 257
Quotient of polynomial matrices, right 271
Rank factorization of a matrix 60 88
Rank inequalities 61
Rank of a column 12 233
Rank of a matrix 12 58 269
Rank of a polynomial matrix 217 269
Rank of a row 12 272
Ratio rule for derivatives 174 176 208
Rational matrix 269
Rayleigh ratio 269
Rayleigh — Ritz theorem 67 133 159
Real matrix 1 269
Real matrix, negative definite 151
Real matrix, negative semidefinite 151
Real matrix, positive definite 150
Real matrix, positive semidefinite 151
Real polynomial matrix 217 269
Rectangular matrix 270
Reducible matrix 270
Reflexive generalized inverse matrix 270
Regular matrix 10 253 263 270
Regular polynomial matrix 218 270
Relatively left prime polynomial matrices 219 256 270
Relatively prime polynomials 212
Relatively right prime polynomial matrices 219 270 271
Resultant 212
Resultant matrix 270
Reverse unit matrix 270
Riccati equation 271
Right coprime polynomial matrices 219 270 271
Right divisibility of a polynomial matrix 219 271
Right divisor of a polynomial matrix 219 271
Right eigenvector 271
Right inverse matrix 271
Right multiple of a polynomial matrix 218 271
Right quotient of polynomial matrices 218 271
Right remainder of polynomial matrices 219 271
Root of a polynomial 211
Root of a polynomial, multiplicity of 211
Rotation matrix 272
Routh matrix 272
Row dimension of a matrix 1 272
Row rank of a matrix 12 272
Row regular matrix 272
Row stochastic matrix 272 277
Row vector 2 272
Row vectorization of a matrix 272
Row vectorization operator 96
Row-sum norm 103
Row-sum norm, properties of 110
Scalar matrix 273
Scalar multiplication 3 18 273
Scalar product 273
Schur complement of a matrix 273
Schur decomposition 69 86
Schur decomposition, of real matrix 92
Schur norm 103
Schur product 3 273
Schur product theorem 21 152
Schur's inequality 43
Schur-stochastic matrix 273 282
Secondary diagonal of a matrix 273
Self-adjoint matrix norm 102
Selfadjoint matrix 273
Semicirculant matrix 274
Semidefinite matrix 274
Seminegative matrix 274
Seminorm 101 274
Semiorthogonal matrix 274
Semipositive matrix 274
Shift matrix 274
Similar matrices 216 275
Simple eigenvalue 63 275
Simple matrix 114 138 275
Simultaneous diagonalization of Hermitian matrices 86 137
Simultaneous diagonalization of matrices 86 275
Simultaneous diagonalization of positive definite and Hermitian matrices 86 137 155
Simultaneous diagonalization of positive definite and symmetric matrices 86 92 155 163
Sine of a matrix 215 275
Singular matrix 275
Singular value 13 63 64 78 275
Singular value decomposition 60 79 80 85
Singular value of real matrix 91
Singular value, inequalities 80
Skew prime polynomial matrices 219 276
Skew-circulant matrix 275
Skew-Hermitian matrix 131 276
Skew-Hermitian matrix, properties of 131
Skew-symmetric matrix 156 276
Skew-symmetric matrix, properties of 156
Skew-symmetric part of a matrix 276
Smith canonical form 222
Smith normal form 222
Sparse matrix 276
Spectral decomposition 69 70 85 90 137 163
Spectral decomposition of a Hermitian matrix 70 85 137
Spectral decomposition of a normal matrix 69 85
| Spectral decomposition of a real symmetric matrix 70 90
Spectral decomposition of a symmetric matrix 163
Spectral norm 104
Spectral norm, properties of 110
Spectral radius 64 76 139 276
Spectral radius, properties of 141
Spectrum of a matrix 64 276
Square matrix 2 269 276
Square matrix, index of 252
Square matrix, inertia of 252
Square root decomposition 155
Square root decomposition of a real matrix 155
Square root of a matrix 8 276
Stable matrix 119 277
Stable matrix, properties of 119
Stein's theorem 120
Stieltjes matrix 277
Stochastic matrix 139 272 277
Stochastic matrix, doubly 240
Stochastic matrix, properties of 139
Strictly lower triangular matrix 277
Strictly lower triangular matrix, properties of 164
Strictly triangular matrix 277
Strictly triangular matrix, properties of 164 167
Strictly upper triangular matrix 277
Strictly upper triangular matrix, properties of 164
Striped matrix 277
SubMatrix 1 278
Submatrix, principal 268
Submultiplicative norm 102 262 278
Subtraction of matrices 3 278
Sum, direct 4 22 239
Sum, Kronecker 256
Sum, of matrices 3 15
Sup norm 102 264
Sylvester matrix 213 278
Sylvester's law 61
Symmetric matrix 11 156 278
Symmetric matrix, decomposition of 163
Symmetric matrix, derivatives of 185 193
Symmetric matrix, eigenvalues of 158
Symmetric matrix, properties of 156
Symmetric part of a matrix 279
Symmetric r-Toeplitz matrix 279
Symmetric Toeplitz matrix 279
Tensor product 3 279
Theorem, Cayley — Hamilton 67 216
Theorem, Courant — Fischer 67 68 133 159
Theorem, Hopfs 78 142
Theorem, Hurwitz 217
Theorem, inclusion principle 73 135 160
Theorem, Poincarc's separation 74 136 161
Theorem, Pythagoras 104
Theorem, Rayleigh — Ritz 67 133 159
Theorem, Schur product 152
Theorem, Stein's 120
Theorem, Weyl's 75 136 162
Toeplitz matrix 114 279
Toeplitz matrix, block 229
Toeplitz matrix, symmetric 279
Totally nonnegative matrix 280
Totally positive matrix 280
Trace of a matrix 4 41 280
Trace of a matrix, derivatives of 177
Trace of a matrix, inequalities 43
Trace of a matrix, optimization of 45
Transition matrix 277 280
Transpose of a matrix 5 23 280
Transposition matrix 281
Triangle inequality 101
Triangular factorization of a matrix 60 87
Triangular factorization of a nonsingular matrix 87
Triangular matrix 11 281
Triangular matrix, block 230
Triangular matrix, derivatives of 187 195
Triangular matrix, lower 164 259
Triangular matrix, lower block 258
Triangular matrix, properties of 164
Triangular matrix, strictly 164 277
Triangular matrix, strictly lower 277
Triangular matrix, strictly upper 277
Triangular matrix, unit 282
Triangular matrix, unit lower 282
Triangular matrix, unit upper 282
Triangular matrix, upper 164 283
Triangular matrix, upper block 283
Tridiagonal matrix 140 281
Tridiagonal matrix, block 230
Tripotent matrix 281
Unimodular integer matrix 281
Unimodular polynomial matrix 218 254 281
Unipotent matrix 281
Unit lower triangular matrix 282
Unit matrix 2 282
Unit triangular matrix 282
Unit upper triangular matrix 282
Unit vector 282
Unitarily equivalent matrices 282
Unitarily invariant norm 102
Unitarily similar matrices 282
Unitary matrix 11 282
Unitary matrix, properties of 167
Unitary stochastic matrix 27 3 282
Unstable polynomial 212
Upper block triangular matrix 283
Upper Hessenberg matrix 283
Upper triangular matrix 11 281 283
Upper triangular matrix, properties of 164
Vandermonde determinant 49 283
Vandermonde matrix 284
Vec operator 8 95 97 123 128 284
Vech operator 8 96 99 123 128 284
Vector 2
Vector derivatives 171
Vector norm 101 285
Vector polynomial 285
Vector product 285
Vector, characteristic 64
Vector, column 2 233
Vector, gradient 171 247
Vector, length of 257 261
Vector, modulus of 257 261
Vector, null 264
Vector, row 2 272
Vector, unit 282
Vector, zero 286
Vectorization of a column 233
Vectorization of a half 248
Vectorization of a matrix 8 95 233 285
Vectorization of a row 272
Vectorization operator 95
Vectorization operator, column 95
Vectorization operator, row 96
Vectors, dependent 237
Vectors, independent 252
Vectors, linearly dependent 258
Vectors, linearly independent 258
Vectors, orthogonal 265
Vectors, orthonormal 265
Weyl's theorem for eigenvalues 75 136 162
Zero matrix 10 264 286
Zero vector 264 286
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