A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensors

TL;DR

This paper investigates the geometric simplicity of the spectral radius in nonnegative irreducible tensors, establishing conditions under which it is guaranteed to be real and simple, with implications for tensor spectral theory.

Contribution

It provides new theoretical results on the geometric simplicity of the spectral radius for nonnegative irreducible tensors, including cases of odd order and complex tensors.

Findings

Spectral radius of even order nonnegative irreducible tensors is real and geometrically simple.

Conditions are established for the spectral radius to be geometrically simple in odd order or complex tensors.

Results extend understanding of spectral properties of nonnegative tensors.

Abstract

We prove that the spectral radius of even order nonnegative irreducible tensors is real geometrically simple. In the case when the order of the tensor is odd, or in the complex field, some conditions are given to guarantee the geometric simplicity of the spectral radius.