Singular value inequalities of matrices via increasing functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-03 DOI:10.1186/s13660-024-03193-3

Wasim Audeh, Anwar Al-Boustanji, Manal Al-Labadi, Raja’a Al-Naimi

引用次数: 0

Abstract

Let A, B, X, and Y be $n\times n$ complex matrices such that A is self-adjoint, $B\geq 0$ , $\pm A\leq B$ , $\max ( \Vert X \Vert ^{2}, \Vert Y \Vert ^{2} ) \leq 1$ , and let f be a nonnegative increasing convex function on $[ 0,\infty ) $ satisfying $f(0)=0$ . Then $$ 2s_{j}\bigl(f \bigl( \bigl\vert XAY^{\ast } \bigr\vert \bigr) \bigr)\leq \max \bigl\{ \Vert X \Vert ^{2}, \Vert Y \Vert ^{2} \bigr\} s_{j}\bigl(f(B+A)\oplus f(B-A)\bigr) $$ for $j=1,2,\ldots,n$ . This singular value inequality extends an inequality of Audeh and Kittaneh. Several generalizations for singular value and norm inequalities of matrices are also given.

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通过递增函数的矩阵奇异值不等式

让 A, B, X 和 Y 是 $n\times n$ 复数矩阵，使得 A 是自相关的，$B\geq 0$ , $pm A\leq B$ , $\max ( \Vert X \Vert ^{2}, \Vert Y \Vert ^{2} ) \leq 1$ , 并让 f 是一个在 $[ 0,\infty ) $ 上满足 $f(0)=0$ 的非负递增凸函数。Then $$ 2s_{j}\bigl(f \bigl\vert XAY^{\ast } \bigr\vert \bigr) \bigr)\leq \max \bigl\{ \Vert X \Vert ^{2}, \Vert Y \Vert ^{2}.\s_{j}\bigl(f(B+A)\oplus f(B-A)\bigr) $$ for $j=1,2,\ldots,n$ 。这个奇异值不等式扩展了 Audeh 和 Kittaneh 的不等式。此外，还给出了矩阵奇异值不等式和规范不等式的几种一般化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.