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
收藏
页码：140 / 171
页数：32
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