Non-negative matrices and their structured singular values
https://doi.org/10.26907/0021-3446-2023-10-36-45
Abstract
In this article, we present new results for the computation of structured singular values of non-negative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix (M∆). The presented new results on the equivalence of structured singular values, non-negative spectral radius and non-negative determinant of (M∆) is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of (M∆), 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∆).
About the Authors
M. Rehman
Bukhara State University
Uzbekistan
Uzbekistan
Mutti-Ur Rehman.
11 M. Ikbol str., Bukhara, 200118
T. H. Rasulov
Bukhara State University
Uzbekistan
Uzbekistan
Tulkin H. Rasulov.
11 M. Ikbol str., Bukhara, 200118
B. R. Aminov
Akfa University
Uzbekistan
Uzbekistan
Bekzod R. Aminov.
264 Milliy Bog str., Tashkent, 111221
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Review
For citations:
Rehman M., Rasulov T.H., Aminov B.R. Non-negative matrices and their structured singular values. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2023;(10):36-45. (In Russ.) https://doi.org/10.26907/0021-3446-2023-10-36-45
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