Numerical range for weighted Moore-Penrose inverse of tensor

12/21/2022
by   Aaisha Be, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/20/2021

Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system

This paper establishes some perturbation analysis for the tensor inverse...
research
09/30/2019

Biquadratic Tensors, Biquadratic Decomposition and Norms of Biquadratic Tensors

Biquadratic tensors play a central role in many areas of science. Exampl...
research
02/08/2023

Block Diagonalization of Quaternion Circulant Matrices with Applications to Quaternion Tensor Singular Value Decomposition

It is well-known that a complex circulant matrix can be diagonalized by ...
research
11/09/2020

Tensor Completion via Tensor QR Decomposition and L_2,1-Norm Minimization

In this paper, we consider the tensor completion problem, which has many...
research
05/06/2020

Further results on weighted core-EP inverse of matrices

In this paper, we introduce the notation of E-weighted core-EP and F-wei...
research
02/10/2020

Characterization and Representation of Weighted Core Inverse of Matrices

In this paper, we introduce new representation and characterization of t...
research
08/31/2023

Moore-Penrose Dagger Categories

The notion of a Moore-Penrose inverse (M-P inverse) was introduced by Mo...

Please sign up or login with your details

Forgot password? Click here to reset