On weakly irreducible nonnegative tensors and interval hull of some classes of tensors

TL;DR

This paper investigates properties of weakly irreducible nonnegative tensors, establishing spectral radius monotonicity, conditions for interval hulls to be strong $\

Contribution

It introduces new criteria for interval hulls of tensors to be within strong $\

Findings

Spectral radius of weakly irreducible nonnegative tensors is strictly monotonic.

Provides necessary and sufficient conditions for interval hulls to be strong $\

Establishes properties of $\

Abstract

In this article we prove the strict monotonicity of the spectral radius of weakly irreducible nonnegative tensors. As an application, we give a necessary and sufficient condition for an interval hull of tensors to be contained in the set of all strong $\mathcal{M}$-tensors. We also establish some properties of $\mathcal{M}$-tensors. Finally, we consider some problems related to interval hull of positive (semi)definite tensors and $P(P_0)$-tensors.