Coprime factorizations of multivariate rational matrices
type: Item
instance of: scholarly article
title: Coprime factorizations of multivariate rational matrices
zbMATH Open document ID: 0964.93053
DOI: 10.1007/PL00009862
author: E. Zerz
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2001-06-24T00:00:00Z
review text: Coprime factorizations of rational matrices of one variable are extensively used in one-dimensional systems theory. When passing to more than one independent variables, several nonequivalent generalizations of the coprimeness notion appear. In the paper under review, the generalized version of factor coprimeness for polynomial matrices in several variables is considered. In this setting, two polynomial matrices \(D, N\) are left coprime iff the block matrix \([\begin{matrix} N -D\end{matrix} ]\) is a minimal left annihilator. The author describes an algorithm for obtaining a left coprime factorization of a given rational matrix. Certain properties of coprime factorizations are established.
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 1495918
zbMATH Keywords: coprime factorization
zbMATH Keywords: multivariate polynomial matrices
zbMATH Keywords: minimal annihilators
zbMATH Keywords: determinantal ideals
Wikidata QID: Q114232448
reviewed by: Dmitry Kaliuzhnyi-Verbovetskyi
MaRDI profile type: Publication
full work available at URL: pl00009862
OpenAlex ID: W2023709433
description: scientific article; zbMATH DE number 1495918