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Research Article | Open Access

Some new characterizations of the normality for group invertible matrices

Zhirong Guo1, Qianglian Huang2( )
College of Mathematics, Yangzhou Vocational University, Yangzhou 225009, China
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
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Abstract

Normal matrices are an important class of matrices; many authors discuss the normality of matrices. In terms of projection matrices, the inverse of matrices, one-sided X-equality, and X-idempotency of matrices, many new characterizations of normal matrices are obtained in this paper. It may be the first time that the projection, one-sided X-equality, and one-sided X-idempotency are used to characterize the normality of matrices.

Keywords

normal matrixgroup invertible matrixMoore-Penrose inverse matrixprojection
CLC number: 16B99, 16W10

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AIMS Mathematics
Volume 10 Issue 5,
May 2025
Pages 12135-12148
DOI: 10.3934/math.2025550

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Cite this article:
Guo Z, Huang Q. Some new characterizations of the normality for group invertible matrices. AIMS Mathematics, 2025, 10(5): 12135-12148. https://doi.org/10.3934/math.2025550

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Received: 30 March 2025
Revised: 06 May 2025
Accepted: 13 May 2025
Published: 15 May 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)