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Research Article | Open Access

Some matrix inequalities related to norm and singular values

Xiaoyan Xiao1, Feng Zhang1( ), Yuxin Cao2, Chunwen Zhang2
Department of Mathematics, Southeast University Chengxian College, Nanjing 210000, China
Department of Electrical and Computer Engineering, Southeast University Chengxian College, Nanjing 210000, China
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Abstract

In this short note, we presented a new proof of a weak log-majorization inequality for normal matrices and obtained a singular value inequality related to positive semi-definite matrices. What's more, we also gave an example to show that some conditions in an existing norm inequality are necessary.

Keywords

singular valuesweak log-majorizationnormal matrices
CLC number: 47A30, 15A42, 15A18

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 4205-4210
DOI: 10.3934/math.2024207

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Cite this article:
Xiao X, Zhang F, Cao Y, et al. Some matrix inequalities related to norm and singular values. AIMS Mathematics, 2024, 9(2): 4205-4210. https://doi.org/10.3934/math.2024207

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Received: 20 November 2023
Revised: 27 December 2023
Accepted: 04 January 2024
Published: 15 February 2024
©2024 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)