Nonnegative Matrices and Their Structured Singular Values

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-01-09 DOI:10.3103/s1066369x23100080

M. Rehman, T. Rasulov, B. Aminov

引用次数: 0

Abstract

In this article, we present new results for the computation of structured singular values of nonnegative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix \((M\vartriangle )\). The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant of \((M\vartriangle )\) is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of \((M\vartriangle )\), both structured singular values and spectral radius are exactly equal. Finally, we present the exact equivalence between structured singular value and the largest singular value of \((M\vartriangle )\).

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非负数矩阵及其结构奇异值

摘要在本文中，我们提出了计算受纯复扰动的非负矩阵的结构奇异值的新结果。我们证明了结构奇异值和扰动矩阵（(M\vartriangle )\）谱半径的等价性。提出并分析了关于结构奇异值、非负谱半径和 \((M\vartriangle )\) 的非负行列式等价性的新结果。此外，我们还证明了对于单位谱半径的 \((M\vartriangle )\), 结构奇异值和谱半径是完全相等的。最后，我们提出了结构奇异值和\( （M （vartriangle ）\）的最大奇异值之间的精确等价关系。

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

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.