On minimial factorizations of rational matrix functions
type: Item
instance of: scholarly article
title: On minimial factorizations of rational matrix functions
zbMATH Open document ID: 0542.47010
DOI: 10.1007/BF01691919
author: Nir Cohen
published in: Integral Equations and Operator Theory
publication date: 1983-01-01T00:00:00Z
review text: The theory of factorization of rational \(n\times n\) matrix functions \(W(\lambda)=D+C(\lambda -A)^{-1}B,\) as developed by \textit{H. Bart}, \textit{I. Gohberg} and \textit{M. A. Kaashoek} [Minimal factorization of matrix and operator functions (1979; Zbl 0424.47001)], is extended to the case where \(D=W(\infty)\) is not invertible. This extension requires a generalization of the notion of a supporting projection and includes a description of all minimal factorizations of which the factors are again square rational matrix functions. Special attention is paid to spectral factorizations, stable factorizations and to the case when \(\det W(\lambda)\not\equiv {\text{ß}}.\) As an application a new proof is given of the Gohberg- Lancaster-Rodman factorization theorem for monic matrix polynomials.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 3861838
zbMATH Keywords: factorization of rational \(n\times n\) matrix functions
zbMATH Keywords: supporting projection
zbMATH Keywords: minimal factorizations
zbMATH Keywords: spectral factorizations
zbMATH Keywords: stable factorizations
zbMATH Keywords: Gohberg-Lancaster-Rodman factorization theorem for monic matrix polynomials
Wikidata QID: Q114233934
MaRDI profile type: Publication
cites work: Spectral analysis of matrix polynomials. I. Canonical forms and divisors
cites work: Q5659396
full work available at URL: https://doi.org/10.1007/bf01691919
OpenAlex ID: W2075094763
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description: scientific article; zbMATH DE number 3861838