NUMERICAL RANGE FOR WEIGHTED MOORE-PENROSE INVERSE OF TENSOR

被引：0

作者：

Be, Aaisha ^{[1
]}

Shekhar, Vaibhav ^{[2
,3
]}

Mishra, Debasisha ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Raipur 492010, India

[2] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

[3] Govt Engn Coll, Dept Appl Sci & Humanities, Sheikhpura 811105, Bihar, India

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2024年 / 40卷

关键词：

Tensor; Einstein product; Numerical range; Numerical radius; Weighted Moore-Penrose inverse; MATRICES; RADIUS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 matrix setting.

引用

页码：140 / 171

页数：32

共 57 条

[51] Outer and (b,c) inverses of tensors [J].