On the joint spectral radius of a nilpotent Lie algebra of matrices

TL;DR

This paper extends a spectral radius formula to complex nilpotent Lie algebras of matrices, generalizing a known result for commuting matrices, and provides insights into their spectral properties.

Contribution

It introduces a spectral radius formula for nilpotent Lie algebras of matrices, broadening the understanding beyond commuting matrices.

Findings

Spectral radius formula established for nilpotent Lie algebras.

Extension of known results from commuting matrices to nilpotent Lie algebras.

Provides a basis-dependent spectral analysis for these algebras.

Abstract

For a complex nilpotent finite dimensional Lie algebra of matrices,and a Jordan-H\"older basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.