Geodesic
Non-negative matrices and their structured singular values
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 36-45

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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 $(M\triangle)$. The presented new results on the equivalence of structured singular values, non-negative spectral radius and non-negative determinant of $(M\triangle)$ is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of $(M\triangle)$, 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 $(M\triangle)$.
Keywords: $\mu$-values, singular values, eigen values, structured matrices. 
@article{IVM_2023_10_a2,
     author = {M. Rehman and T. Rasulov and B. Aminov},
     title = {Non-negative matrices and their structured singular values},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--45},
     publisher = {mathdoc},
     number = {10},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_10_a2/}
}
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M. Rehman; T. Rasulov; B. Aminov. Non-negative matrices and their structured singular values. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 36-45. http://geodesic.mathdoc.fr/item/IVM_2023_10_a2/