Work

Decompositions of periodic matrices into a sum of special matrices

Year: 2025

Type: article

Abstract: We study the problem of when a periodic square matrix of order $n\times n$ over an arbitrary field $\mathbb{F}$ is decomposable into the sum of a square-zero matrix and a torsion matrix and show that this decomposition can always be obtained for matrices of rank at least $\frac{n}{2}$ when $\mathbb{F}$ is either a field of prime characteristic, or the field of rational numbers, or an algebraically closed field of zero characteristic. We also provide a counterexample to such a decomposition when $\mathbb{F}$ equals the field of the real numbers.

Source: Electronic Journal of Linear Algebra

DOI: 10.13001/ela.2025.9099

Authors: Peter Danchev, Esther García, Miguel Gómez Lozano

Institutions: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Universidad Rey Juan Carlos, Universidad de Málaga

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Universidad Rey Juan Carlos, Junta de Andalucía, Agencia Estatal de Investigación

Award: G1737173237