Products of Hermitian matrices over division rings

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-11 DOI:10.1016/j.laa.2025.02.016

Peeraphat Gatephan , Kijti Rodtes

引用次数: 0

Abstract

In this paper, we investigate the Dieudonné determinant of Hermitian matrices over division rings with involution. We prove that every matrix over division rings whose center contains at least

n + 2

elements can be expressed as a product of three diagonalizable matrices. Moreover, we establish necessary and sufficient conditions for matrices to be factored into a product of a finite number of Hermitian matrices over division rings and one diagonalizable matrix for which its Dieudonné determinant is the commutator class containing one. As a consequence, Radjavi's factorization over complex numbers and over the real quaternion division ring can be obtained immediately.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.