Abstract
In this paper, we give new singular value inequalities for matrices. It is shown that if A, B, X are \(n\times n\) matrices such that X is positive semidefinite, and if \(f:[0,\infty )\rightarrow {\mathbb {R}} \) is an increasing nonnegative convex function, then
and
for \(j=1,2,...,n\). Some of our inequalities present refinements of some known singular value inequalities.
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Communicated by Qing-Wen Wang.
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Al-Natoor, A., Hirzallah, O. & Kittaneh, F. Singular value inequalities for convex functions of positive semidefinite matrices. Ann. Funct. Anal. 14, 7 (2023). https://doi.org/10.1007/s43034-022-00233-1
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DOI: https://doi.org/10.1007/s43034-022-00233-1
Keywords
- Singular value
- Spectral norm
- Unitarily invariant norm
- Positive semidefinite matrix
- Convex function
- Inequality