An extension of Yamamoto's theorem on the eigenvalues and singular values of a matrix

Abstract

We extend, in the context of real semisimple Lie group, a result of T. Yamamoto which asserts that lim_m→∞[s_i(X^m)]^1/m = |λ_i(X)|, i=1,…,n, where s₁(X)≥…≥s_n(X) are the singular values, and λ₁(X),…,λ_n(X) are the eigenvalues of the n×n matrix X, in which |λ₁(X)|≥…≥|λ_n(X)|.