A note on numerical ranges of tensors
Abstract
Theory of numerical range and numerical radius for tensors is not studied much in the literature. In 2016, Ke {\it et al.} [Linear Algebra Appl., 508 (2016) 100-132] introduced first the notion of numerical range of a tensor via the -mode product. However, the convexity of the numerical range via the -mode product was not proved by them. In this paper, the notion of numerical range and numerical radius for even-order square tensors using inner product via the Einstein product are introduced first. We provide some sufficient conditions using numerical radius for a tensor to being unitary. The convexity of the numerical range is also proved. We also provide an algorithm to plot the numerical range of a tensor. Furthermore, some properties of the numerical range for the Moore--Penrose inverse of a tensor are discussed.
Keywords
Cite
@article{arxiv.2108.08154,
title = {A note on numerical ranges of tensors},
author = {Nirmal Chandra Rout and Krushnachandra Panigrahy and Debasisha Mishra},
journal= {arXiv preprint arXiv:2108.08154},
year = {2025}
}
Comments
20 pages