Inequalities for numerical invariants of sets of matrices

Abstract

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 and Wang as an immediate corollary.

10 pages. Results and presentation slightly improved

Cited by in corpus (11)

• Mather sets for sequences of matrices and applications to the study of joint spectral radii
• The Berger-Wang formula for the Markovian joint spectral radius
• On accuracy of approximation of the spectral radius by the Gelfand formula
• On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
• Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
• The joint spectrum
• A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
• On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
• The joint spectral radius is pointwise Hölder continuous
• A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
• A height gap in $G{L}_d(\overline{\mathbb{Q}})$ and almost laws