Some new characterizations of the normality for group invertible matrices

Zhirong Guo; Qianglian Huang; Zhirong Guo; Qianglian Huang

doi:10.3934/math.2025550

AIMS Mathematics

2025, Volume 10, Issue 5: 12135-12148. doi: 10.3934/math.2025550

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Some new characterizations of the normality for group invertible matrices

Zhirong Guo ¹,
Qianglian Huang ^{2
,
,}

1.
College of Mathematics, Yangzhou Vocational University, Yangzhou 225009, China
2.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Received: 30 March 2025 Revised: 06 May 2025 Accepted: 13 May 2025 Published: 27 May 2025
MSC : 16B99, 16W10

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.
- normal matrix,
- group invertible matrix,
- Moore-Penrose inverse matrix,
- projection
Citation: Zhirong Guo, Qianglian Huang. Some new characterizations of the normality for group invertible matrices[J]. AIMS Mathematics, 2025, 10(5): 12135-12148. doi: 10.3934/math.2025550

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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.

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