The Minc-type bound and the eigenvalue inclusion sets of the general product of tensors

TL;DR

This paper introduces new bounds for the spectral radius and eigenvalue inclusion sets of the general tensor product, extending the Minc-type bound to nonnegative tensors and providing tools for spectral analysis.

Contribution

It presents the first Minc-type bound for the spectral radius of nonnegative tensors and new bounds for eigenvalues of their general product.

Findings

Established Minc-type bound for nonnegative tensors' spectral radius

Derived bounds for eigenvalue inclusion sets of tensor products

Extended spectral analysis tools to tensor algebra

Abstract

In this paper, we give the Minc-type bound for spectral radius of nonnegative tensors. We also present the bounds for the spectral radius and the eigenvalue inclusion sets of the general product of tensors.