Complementary basic matrices
type: Item
instance of: scholarly article
title: Complementary basic matrices
zbMATH Open document ID: 1059.15026
author: Miroslav Fiedler
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: This paper is a continuation of the author's paper [ibid. 373, 143--151 (2003; Zbl 1033.15010)]. The subdiagonal rank of a square matrix is defined as the order of the maximal nonsingular submatrix all of whose entries are subdiagonal, and the superdiagonal rank is defined analogously. A square matrix having both sub- and superdiagonal ranks \(\geq 1\) is called basic. In the earlier paper the author studied primarily basic matrices with LU-decomposition, while in this paper the author studies so-called complementary basic matrices without the extra condition. The main result of the earlier paper is a certain factorization of basic matrices with LU-decomposition. In this paper the author generalizes this result to complementary basic matrices and proves that the converse holds as well.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2083501
zbMATH Keywords: subdiagonal rank
zbMATH Keywords: basic matrix
zbMATH Keywords: zig-zag shape
zbMATH Keywords: factorization
zbMATH Keywords: superdiagonal rank
zbMATH Keywords: LU-decomposition
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: j.laa.2004.01.014
OpenAlex ID: W2131079143
cites work: A Class of Hessenberg Matrices with Known Eigenvalues and Inverses
cites work: Structure ranks of matrices
cites work: Basic matrices.
cites work: A note on companion matrices
DOI: 10.1016/J.LAA.2004.01.014
Recommended article: MAX algebraic complementary basic matrices
Recommended article: Combinatorial aspects of generalized complementary basic matrices
Recommended article: A new characterization of generalized complementary basic matrices
Recommended article: Some inheritance properties for complementary basic matrices
Recommended article: On complementary matrix algebras
Recommended article: Q4936535
Recommended article: Q3550071
Recommended article: Inverse complements of a matrix and applications
Recommended article: Permanents, determinants, and generalized complementary basic matrices
Recommended article: Q2993876
description: scientific article; zbMATH DE number 2083501