Non-negative matrices and their structured singular values

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 $(M\triangle)$.