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| Iohvidov I.S. — Hankel and Toeplitz Matrices and Forms |
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| Предметный указатель |
Basis 19
Basis, orthonormal 21
Basis, orthonormal, consisting of eigenvectors 21
Bezoutiant 176
Canonical representation 28
Cauchy index 200
Characteristic of a Hankel matrix 63
Characteristic of a Toeplitz matrix l08
Class  94
Class  133
Complement, orthogonal 22
Defect of a Hankel matrix 78
Defect of a Toeplitz matrix 125
Diagonal, “wrong” 63 l08
Discriminant of a form 28
Eigenvalue of a Hermitian form 28
Eigenvalue of a linear operator 19
Eigenvalue of a matrix 18
Eigenvector 19
Element, “wrong” 72 l08
Extension of a Hankel matrix 53
Extension of a Hankel matrix, singular 54
Extension of a Hankel matrix, singular, real 60
Extension of a Toeplitz matrix 96
Extension of a Toeplitz matrix, singular 97
Extension of a Toeplitz matrix, singular, Hermitian 98
Extension of a Toeplitz matrix, singular, real 99
Extension of a Toeplitz matrix, singular, symmetric 99
Extension, uniqueness of singular 56 101
Form, degenerate (singular) 28
Form, Hankel 81
Form, Hermitian 24
Form, Hermitian, Toeplitz 127
Form, nondegenerate (regular) 28
Form, nonnegative 30
Form, positive definite 30
Form, quadratic 31
Form, real Toeplitz (quadratic) 127 212
Form, truncated 33
Formula, interpolation of Lagrange 204
Formula, Sylvester 42
Functionals C and S 201
Identity, basic, for truncated forms 33
Identity, Kronecker 44
Identity, Sylvester 6
Independent Hankel forms 214
Inertia, law of 26
Invariant subspace 22
Invariants of a form 28
Inversion of block “quasitriangular” matrices 161
Inversion of Hankel matrices 170
Inversion of Toeplitz matrices 147
Isolated group of zeros 81 127
Isolated zero 48
Law of inertia 26
Lemma on the “translation” l04
Linear operator 19
Linear operator, Hermitian 21
Matrix, antitransposed 143
Matrix, block-Toeplitz 175
Matrix, block-“quasitriangular” 161
Matrix, Hankel 53
Matrix, Hankel, Hermitian 53
Matrix, Hankel, infinite 53
Matrix, Hankel, real 53
Matrix, involution 137
Matrix, of a linear operator 19
Matrix, reciprocal 2
| Matrix, Toeplitz 96
Matrix, Toeplitz, Hermitian 96
Matrix, Toeplitz, infinite 97
Matrix, Toeplitz, real 99
Matrix, Toeplitz, symmetric l02
Matrix, triangular 5
Matrix, unitary 137
Method of comparison (of extensions) 54 62 l07
Method of Jacobi 44
Minor, bordered 5
Minor, complementary 1
Minor, of the reciprocal matrix 2
Minor, pricipal 119
Minors, successive principal 33
Moment problem, polynomial 202
Moment problem, trigonometrical 208
Multiplication of block matrices 163
Newton formulae 201
Newton sums 192
Nonsingularity, strict 175
Polynomial, characteristic 19
Polynomial, Hennitian-symmetrical 192
Polynomial, orthogonal with respect to the axis 216
Polynomial, quasiorthogonal 203
Polynomial, real 192
Polynomial, real, trigonometrical 202
Polynomial, trigonometrical 202
Polynomial, with respect to the unit circle 217
Quasipolynomial 206
Rank of a form 24
Rank of a Hankel matrix 71
Rank of a Toeplitz matrix 117
Rank of an infinite matrix 74
Rational function 201
Recalculation of the characteristics 137
Roots of polynomials as continuous functions 19
Roots of polynomials, complex conjugated 192
Roots of polynomials, mirror-like 192
Roots of polynomials, multiple 19 193
Rule for the signature of Toeplitz forms 129
Rule, Frobenius' 49
Rule, Frobenius', for the signature of Hankel forms 90
Rule, Gundelfingers 48
Rule, Jacobi's 47
Rule, Jacobi's, generalizations of 48
Scalar product 20
Signature 28
Spectrum of a linear operator 19
Spectrum of a matrix 19
Squares, independent 25
Squares, negative 27
Squares, positive 27
Subspace, invariant 22
Successive principal minors 33
Symmetric functions 201
Theorem of Borhardt — Jacobi 193
Theorem of Fejer — F. Riesz 206
Theorem of Fischer 205
Theorem of Herglotz — M. Krein 194
Theorem of Kronecker 74 79
Theorem on jumps in the rank 74 121
Theorem, first extension 54 97
Theorem, fundamental, on the signature of a Toeplitz form 129
Theorem, second extension 55 100
Transformation of Fischer — Frobenius 179
Transformation of Hankel into Toeplitz matrices 136
Transformation of Toeplitz into Hankel matrices 135
Uniqueness of singular extensions 56 101
Zero, isolated 48
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