On invertibility of nonsquare generalized Bezoutians
type: Item
instance of: scholarly article
title: On invertibility of nonsquare generalized Bezoutians
zbMATH Open document ID: 0827.15028
DOI: 10.1016/0024-3795(94)00310-A
published in: Linear Algebra and its Applications
publication date: 1995-12-13T00:00:00Z
review text: Für quadratische verallgemeinerte Bezout-Matrizen, die durch vier Matrixpolynome mit nicht notwendig quadratischen Matrizen bestimmt sind, werden notwendige und hinreichende Invertierbarkeitskriterien bewiesen. Vorbereitend werden hierzu Bedingungen für die einseitige Invertierbarkeit nicht-quadratischer Bezout-Matrizen hergeleitet. Als Anwendung ergeben sich Invertierbarkeitsaussagen für Block-Hankel- Matrizen. Speziell werden Formeln für die Inversen von Hermiteschen Block-Hakel-Matrizen hergeleitet, die lediglich zwei Block-Spalten der Inversen benutzen.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 778257
zbMATH Keywords: invertibility
zbMATH Keywords: nonsquare generalized Bezoutians
zbMATH Keywords: block Hankel matrix
zbMATH Keywords: matrix inversion
zbMATH Keywords: matrix polynomial
author: Michael Gekhtman
author: M. E. Shmoĭsh
reviewed by: Hans-Joachim Kowalsky
MaRDI profile type: Publication
cites work: Hilbert spaces of analytic functions, inverse scattering and operator models. I
cites work: Q3724961
cites work: Generalized Bezoutian and Sylvester matrices in multivariable linear control
cites work: On inversion of block Toeplitz matrices
cites work: On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
cites work: Q3973565
cites work: On the zeros of some continuous analogues of matrix orthogonal polynomials and a related extension problem with negative squares
cites work: Hankel and Loewner matrices
cites work: On symmetric rational transfer functions
cites work: Q3782274
cites work: Q4103681
cites work: Q4775962
cites work: Q4775961
cites work: On inversion of square matrices partitioned into non-square blocks
cites work: On Bézoutians of nonsquare matrix polynomials and inversion of matrices with nonsquare blocks
cites work: Q5313649
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
cites work: Inversion of Toeplitz matrices with only two standard equations
cites work: Q4097423
cites work: The Bezoutian and the eigenvalue-separation problem for matrix polynomials
cites work: Generalized Bezoutian and the inversion problem for block matrices, I. General scheme
cites work: Q5659396
cites work: The theory of V-Bézoutians and its applications
cites work: On generalized spectral functions, the parametrization of block Hankel and block Jacobi matrices, and some root location problems
cites work: Bézoutians of polynomial matrices and their generalized inverses
description: scientific article; zbMATH DE number 778257