Abstract
In this work, we investigate inequalities of singular values and unitarily invariant norms for sums and products of matrices. First, we prove that \(s^{2}\big (XY^{*}\big )\prec _{w\log }s\big ((X^{*}X)^{q}(Y^{*}Y)(X^{*}X)^{1-q}\big )\), where \(X,\ Y\in M_{n}(C)\) and \(0<q<1\). Based on this result, we present some inequalities between sum of the t-geometric mean and sum of the product of matrices. Those obtained results are the generalization of the present results. In the end, we present a singular values version of Audenaert’s inequality [1].
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Zhao, J. Inequalities of singular values and unitarily invariant norms for sums and products of matrices. Positivity 28, 33 (2024). https://doi.org/10.1007/s11117-024-01053-4
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DOI: https://doi.org/10.1007/s11117-024-01053-4