Some matrix inequalities related to norm and singular values

Xiaoyan Xiao; Feng Zhang; Yuxin Cao; Chunwen Zhang; Xiaoyan Xiao; Feng Zhang; Yuxin Cao; Chunwen Zhang

doi:10.3934/math.2024207

AIMS Mathematics

2024, Volume 9, Issue 2: 4205-4210. doi: 10.3934/math.2024207

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Research article Special Issues

Some matrix inequalities related to norm and singular values

1.
Department of Mathematics, Southeast University Chengxian College, Nanjing 210000, China
2.
Department of Electrical and Computer Engineering, Southeast University Chengxian College, Nanjing 210000, China

Received: 20 November 2023 Revised: 27 December 2023 Accepted: 04 January 2024 Published: 15 January 2024
MSC : 47A30, 15A42, 15A18

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.
- singular values,
- weak log-majorization,
- normal matrices
Citation: Xiaoyan Xiao, Feng Zhang, Yuxin Cao, Chunwen Zhang. Some matrix inequalities related to norm and singular values[J]. AIMS Mathematics, 2024, 9(2): 4205-4210. doi: 10.3934/math.2024207

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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.

References

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