This article is cited in 2 papers

On some decompositions of matrices over algebraically closed and finite fields

Peter Danchev

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Abstract: Decomposition of every square matrix over an algebraically closed field or over a finite field into a sum of a potent matrix and a nilpotent matrix of order 2 is considered. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022).
The question of when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2 is also completely considered.

Keywords: nilpotent matrix, potent matrix, Jordan normal form, rational form, field.

UDC: 512.6

Received: 22.04.2021
Received in revised form: 29.05.2021
Accepted: 05.06.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-5-547-553

Bibliographic databases:

•