Nonnegative Matrices and Their Structured Singular Values

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 . The presented new results on the equivalence of st...

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Bibliographic Details
Published inRussian mathematics Vol. 67; no. 10; pp. 30 - 38
Main Authors Rehman, M., Rasulov, T., Aminov, B.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2023
Springer Nature B.V
Subjects
Algorithms
Approximation
Determinants
Eigenvalues
Eigenvectors
Equivalence
Iterative methods
Linear algebra
Mathematics
Mathematics and Statistics
Structured singular values
System theory
structured matrices
eigenvalues
singular values
values
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ISSN1066-369X
1934-810X
DOI10.3103/S1066369X23100080

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Summary: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 . The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant of is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of , 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 .
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ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X23100080