On the tubular eigenvalues of third-order tensors

05/10/2023

∙

by   Fatemeh P. A. Beik, et al.

∙

0

∙

share

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative definitions of eigenvalue for third-order tensors that are known in the literature, namely eigentuple and T-eigenvalue. In addition, it establishes a few results on tubular spectra of tensors which can be exploited to analyze the convergence of tubular versions of iterative methods for solving tensor equations.