We prove new inequalities and equalities for the generalized joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means bounded sets positive kernel operators on Banach function spaces. In case non-negative matrices that define sequences, we obtain additional results. Our results extend several authors appeared relatively recently.

Abstract. Distance energy is a newly introduced molecular graph-based analog of the total π-electron energy, and it is defined as the sum of the absolute eigenvalues of the molecular distance matrix. For trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that increases the distance spect...

We propose two simple upper bounds for the joint spectral radius of sets of nonnegative matrices. These bounds, the joint column radius and the joint row radius, can be computed in polynomial time as solutions of convex optimization problems. We show that for general matrices these bounds are within a factor 1/n of the exact value, where n is the size of the matrices. Moreover, for sets of matr...

In this article, we investigate the solution of a new class absolute value equation (NCAVE) A1x ? |B1x c| = d. Based on spectral radius condition, singular condition and row column W-property, some necessary sufficient conditions for unique solvability NCAVE are gained. Some results generalized (NGAVE) A1x?|B1x| d also obtained.