A factorization of totally nonsingular matrices over a ring with identity
type: Item
instance of: scholarly article
title: A factorization of totally nonsingular matrices over a ring with identity
zbMATH Open document ID: 0948.15012
DOI: 10.1016/S0024-3795(99)00223-2
author: Miroslav Fiedler
author: Thomas L. Markham
published in: Linear Algebra and its Applications
publication date: 2000-06-07T00:00:00Z
review text: The authors call a rectangular matrix over a ring with identity totally nonsingular (TNS) if, for all \(k\), all its submatrices having either \(k\) consecutive rows and the first \(k\) columns, or \(k\) consecutive columns and the first \(k\) rows, are invertible. They prove that a matrix is TNS if and only if it admits a certain factorization with bidiagonal-type factors and certain invertible entries. This generalizes a recent result of the authors, namely the factorization of a square matrix over a ring with identity which satisfies the consecutive row and consecutive column properties.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1420038
zbMATH Keywords: totally nonsingular matrices
zbMATH Keywords: ring with identity
zbMATH Keywords: factorization
reviewed by: Rabe von Randow
MaRDI profile type: Publication
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Wikidata QID: Q126977138
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description: scientific article; zbMATH DE number 1420038