Canonical Form of Reduced 3-by-3 Matrix with One Characteristic Root and with Some Zero Subdiagonal Elements-Reference-Cited by-同舟云学术

Canonical Form of Reduced 3-by-3 Matrix with One Characteristic Root and with Some Zero Subdiagonal Elements

Published:2019-06-02 Issue: Volume:2019 Page:1-10
ISSN:2314-4629
Container-title:Journal of Mathematics
language:en
Short-container-title:Journal of Mathematics

Author:

Shavarovskii B. Z.¹^ORCID

Affiliation:

1. Department of Algebra, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Lviv 79060, Ukraine

Abstract

A canonical form for a reduced matrix of order 3 with one characteristic root and with some zero subdiagonal elements is constructed. Thus, the problem of classification with respect to semiscalar equivalence of a selected set of polynomial matrices is solved.

Publisher

Hindawi Limited

Subject

General Mathematics

Link

http://downloads.hindawi.com/journals/jmath/2019/7646132.pdf

Reference15 articles.

1. Reduced Triangular Form of Polynomial 3-by-3 Matrices with One Characteristic Root and Its Invariants

2. On Some “Tame” and “Wild” Aspects of the Problem of Semiscalar Equivalence of Polynomial Matrices

3. Toeplitz Matrices in the Problem of Semiscalar Equivalence of Second-Order Polynomial Matrices

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1. Standard Forms of the Matrices Over Rings with Respect to Various Types of Equivalence and Their Applications to the Theory of Matrix Factorization and Matrix Equations;Journal of Mathematical Sciences;2022-08

2. Reduction to a Canonical Form of a Third-Order Polynomial Matrix with One Characteristic Root by means of Semiscalarly Equivalent Transformations;Journal of Mathematics;2020-10-28

3. Non-singular solutions of one class of matrix equations over a polynomial ring;Prykladni Problemy Mekhaniky i Matematyky;2019-12-24