Numerical range for weighted Moore-Penrose inverse of tensor
Numerical Analysis
2025-08-07 v1 Numerical Analysis
Functional Analysis
Abstract
This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-Penrose inverse of an arbitrary-order tensor. We then define the notions of weighted normal tensor for an even-order square tensor and weighted tensor norm. Finally, we apply these to study the theory of numerical range for the weighted Moore-Penrose inverse of an even-order square tensor and exploit its several properties. We also obtain a few new results in the matrix setting that generalizes some of the existing results as particular cases.
Keywords
Cite
@article{arxiv.2212.10832,
title = {Numerical range for weighted Moore-Penrose inverse of tensor},
author = {Aaisha Be and Vaibhav Shekhar and Debasisha Mishra},
journal= {arXiv preprint arXiv:2212.10832},
year = {2025}
}
Comments
30 pages, 1 figure