Algorithms for simultaneous block triangularization and block diagonalization of sets of matrices-Reference-Cited by-同舟云学术

Algorithms for simultaneous block triangularization and block diagonalization of sets of matrices

Published:2023 Issue:8 Volume:8 Page:19757-19772
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Al-Dweik Ahmad Y.¹,Ghanam Ryad²,Thompson Gerard³,Mustafa M. T.⁴

Affiliation:

1. Department of Mathematics, Birzeit University, Ramallah, Palestine

2. Department of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, Doha 8095, Qatar

3. Department of Mathematics, University of Toledo, Toledo, OH 43606, USA

4. Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar

Abstract

<abstract><p>In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper investigates the more general problem of putting a set of matrices into block triangular or block-diagonal form simultaneously. Based on common invariant subspaces, two algorithms for simultaneous block triangularization and block diagonalization of sets of matrices are presented. As an alternate approach for simultaneous block diagonalization of sets of matrices by an invertible matrix, a new algorithm is developed based on the generalized eigenvectors of a commuting matrix. Moreover, a new characterization for the simultaneous block diagonalization by an invertible matrix is provided. The algorithms are applied to concrete examples using the symbolic manipulation system Maple.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference9 articles.

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