LU-decomposition of a matrix with entries of different kinds
type: Item
instance of: scholarly article
title: LU-decomposition of a matrix with entries of different kinds
zbMATH Open document ID: 0531.15010
DOI: 10.1016/0024-3795(83)90109-X
author: Kazuo Murota
published in: Linear Algebra and its Applications
publication date: 1983-01-01T00:00:00Z
review text: Given a matrix A with entries in a field F, which is extension field of a field K, that has a decomposition \(A=Q+T\) where Q is a matrix with entries in K and all nonzero entries of T are algebraically independent transcendentals over K. It is shown that if det \(A\in K\backslash \{0\}\) then there exist permutation matrices \(P_ r,P_ c\) and an LU- decomposition of \(P_ r^ TAP_ c\) where L,U have the following properties: The elements of L are polynomials of degree at most 1 with coefficients in K in the nonzero entries of T and the entries of U are in K. It is indicated how to find the suitable permutations to achieve this decomposition. The problem of finding an above factorization occured in large-scale systems analysis.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 3842062
zbMATH Keywords: LU-decomposition
zbMATH Keywords: algebraically independent transcendentals
zbMATH Keywords: systems analysis
reviewed by: Volker Mehrmann
MaRDI profile type: Publication
cites work: The maximum-rank minimum-term-rank theorem for the pivotal transforms of a matrix
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description: scientific article; zbMATH DE number 3842062