On products and sums of coninvolutory matrices

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI:10.1016/j.laa.2026.01.009

Daryl Q. Granario

引用次数: 0

Abstract

A complex matrix A is said to be coninvolutory if A is nonsingular and its inverse is its conjugate

\overline{A}

. We show that every complex matrix A with

| \det A | = 1

is a product of four coninvolutory matrices. We also characterize matrices that are products of three coninvolutory matrices. Finally, we give a concanonical form characterization for matrices that are sums of two coninvolutory matrices.

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关于卷积矩阵的积与和

如果一个复矩阵A是非奇异的，并且它的逆是它的共轭A，则称它是共轭的。我们证明了每一个|det (A) |=1的复矩阵A是四个对合矩阵的乘积。我们也描述了矩阵是三个对合矩阵的乘积。最后，我们给出了两个共对合矩阵和的共正则形式的刻划。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.