Minimal indices cancellation and rank revealing factorizations for rational matrix functions
type: Item
instance of: scholarly article
title: Minimal indices cancellation and rank revealing factorizations for rational matrix functions
zbMATH Open document ID: 1179.15013
author: Şerban Sabău
author: Cristian Oară
published in: Linear Algebra and its Applications
publication date: 2009-10-09T00:00:00Z
review text: The authors investigate general rational matrix functions, in particular, they consider their finite and infinite poles and zeros, their partial multiplicities and the left (right) indices of a minimal polynomial basis of the null spaces to the left (right). They concentrate on the left minimal displacement problem and the left rank compression problem. The authors obtain the class of minimal solutions to the minimal indices displacement problem formulated for a completely general rational matrix function. They show that minimal indices can be canceled by an invertible factor that may have arbitrary poles and zeros. They study minimal solutions that feature some symmetry with respect to the imaginary axis or the unit circle and have given necessary and sufficient existence conditions and the class of solutions. They also extend the well-known rank revealing factorization from constant to rational matrices.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 5612556
zbMATH Keywords: rational matrix functions
zbMATH Keywords: rank revealing factorization
zbMATH Keywords: minimal indices cancellation
zbMATH Keywords: J-unitary
zbMATH Keywords: J-inner
zbMATH Keywords: Riccati equations
zbMATH Keywords: matrix pencils
zbMATH Keywords: minimal displacement problem
zbMATH Keywords: left rank compression problem
zbMATH Keywords: minimal solutions
describes a project that uses: SLICOT
MaRDI profile type: Publication
full work available at URL: j.laa.2009.06.019
OpenAlex ID: W2001678265
Wikidata QID: Q114152418
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DOI: 10.1016/J.LAA.2009.06.019
description: scientific article; zbMATH DE number 5612556