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Singular value inequalities and applications

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Abstract

It is shown among other inequalities that if A, B and X are \(n\times n\) complex matrices such that A and B are positive semidefinite, then \(s_{j}(AX-XB)\le \) \(s_{j}\left( \left( \frac{1}{2}A+\frac{1}{2}A^{1/2}\left| X^{*}\right| ^{2}A^{1/2}\right) \oplus \left( \frac{1}{2}B+\frac{1}{2} B^{1/2}\left| X\right| ^{2}B^{1/2}\right) \right) \) for \(j=1,2,\ldots ,2n\). Several related singular value inequalities and norm inequalities are also given.

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Acknowledgements

The author is grateful to the referee for his comments and suggestions.

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  1. Department of Mathematics, Petra University, Amman, Jordan

    Wasim Audeh

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  1. Wasim Audeh
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Audeh, W. Singular value inequalities and applications. Positivity 25, 843–852 (2021). https://doi.org/10.1007/s11117-020-00790-6

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  • DOI: https://doi.org/10.1007/s11117-020-00790-6

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