Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions
type: Item
instance of: scholarly article
title: Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions
zbMATH Open document ID: 0645.15012
DOI: 10.1016/0024-3795(88)90228-5
author: B. George
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: By definition, \(m\times m\) matrices A and Z admit simultaneous reduction to complementary triangular forms if there exists an invertible \(m\times m\) matrix S such that \(S^{-1}AS\) is an upper triangular matrix and \(S^{-1}ZS\) is a lower triangular matrix. Several sufficient conditions for such an S to exist are given. There is a connection with the problem of complete factorization of a transfer function.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 4051807
zbMATH Keywords: minimal factorization
zbMATH Keywords: simultaneous reduction
zbMATH Keywords: complementary triangular forms
zbMATH Keywords: triangular matrix
zbMATH Keywords: complete factorization
zbMATH Keywords: transfer function
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90228-5
OpenAlex ID: W2013102415
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description: scientific article; zbMATH DE number 4051807