Related papers: On the joint spectral radius
We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to…
The primary aim of this paper is to establish bounds on the joint spectral radius for a finite set of nonnegative matrices based on their diagonal elements. The efficacy of this approach is evaluated in comparison to existing and related…
We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger…
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is…
The famous Gelfand formula $\rho(A)= \limsup_{n\to\infty}\|A^{n}\|^{1/n}$ for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is…
In this paper, we present some checkable criteria for the spectral finiteness of a finite subset of the real $d\times d$ matrix space $\mathbb{R}^{d\times d}$, where $2\le d<\infty$.
We realize many sharp spectral bounds of the spectral radius of a nonnegative square matrix $C$ by using the largest real eigenvalues of suitable matrices of smaller sizes related to $C$ that are very easy to find. As applications, we give…
We prove new inequalities for the essential generalized and the essential joint spectral radius of Hadamard (Schur) weighted geometric means of bounded sets of infinite nonnegative matrices that define operators on suitable Banach sequence…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
We study the finite-step realizability of the joint/generalized spectral radius of a pair of real $d\times d$ matrices, one of which has rank 1. Then we prove that there always exists a finite-length word for which there holds the spectral…
We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves…
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part of the paper, we show that any finite set of matrices with at…
The spectral radius {\rho}(G) of a digraph G is the maximum modulus of the eigenvalues of its adjacency matrix. We present bounds on {\rho}(G) that are often tighter and are applicable to a larger class of digraphs than previously reported…
We give a polynomial bound on the spectral density function of a matrix over the complex group ring of Z^d. It yields an explicit lower bound on the Novikov-Shubin invariant associated to this matrix showing in particular that the…
In this article we prove new inequalities for the generalized and the joint spectral radius of bounded sets of positive operators on Banach function and sequence spaces, in particular some inequalities for positive kernel operators that…
We introduce the notion of \emph{joint spectrum} of a compact set of matrices $S \subset GL_d(\mathbb{C})$, which is a multi-dimensional generalization of the joint spectral radius. We begin with a thorough study of its properties (under…
We improve the Cauchy radius of both scalar and matrix polynomials, which is an upper bound on the moduli of the zeros and eigenvalues, respectively, by using appropriate polynomial multipliers.
We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many…
In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact sets of matrices is locally Lipschitz continuous as a function of the matrix set. In the paper, an explicit formula for the related Lipschitz constant is…
The lower spectral radius of a set of $d \times d$ matrices is defined to be the minimum possible exponential growth rate of long products of matrices drawn from that set. When considered as a function of a finite set of matrices of fixed…