Extensions of Yamamoto-Nayak's Theorem

2023/08/08 by Huajun Huang, Huang, Huajun, Tin-Yau Tam +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2308.04101

Abstract

A result of Nayak asserts that \undersetm→ ∞lim |A^m|^1/m exists for each n× n complex matrix A, where |A| = (A^*A)^1/2, and the limit is given in terms of the spectral decomposition. We extend the result of Nayak, namely, we prove that the limit of \undersetm→ ∞lim |BA^mC|^1/m exists for any n× n complex matrices A, B, and C where B and C are nonsingular; the limit is obtained and is independent of B. We then provide generalization in the context of real semisimple Lie groups.

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