Year: 2025
Type: preprint
Abstract: Leveraging tools from convex analysis and incorporating additional singular value information of matrices, we completely resolve the problem of establishing perturbation bounds for the Frobenius norm of subunitary and positive polar factors. We derive corresponding sharp upper and lower bounds. As corollaries, we refine the results of Li and Sun [SIAM J. Matrix Anal. Appl., 23 (2002), pp. 1183--1193] and strengthen the classical Araki-Yamagami inequality [Comm. Math. Phys., 81 (1981), no. 1, pp. 89--96]. The versatility of our method also allows us to strengthen Lee's conjecture, providing a sharper version along with a matching sharp lower bound. Furthermore, we generalize the classical matrix arithmetic-geometric mean inequality and Cauchy-Schwarz inequality into tighter and more robust forms. Finally, we establish a sharp lower bound for a result by Kittaneh [Comm. Math. Phys., 104 (1986), no. 2, pp. 307--310].
Source: arXiv (Cornell University)
Authors: Xu, Zongben, Zhang, Teng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417434033
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