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Iohvidov I.S. — Hankel and Toeplitz Matrices and Forms
Iohvidov I.S. — Hankel and Toeplitz Matrices and Forms

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Название: Hankel and Toeplitz Matrices and Forms

Автор: Iohvidov I.S.

Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 244

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $p_k^H$      94
Class $p_k^{(T)}$      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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