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A note on numerical ranges of tensors.
- Source :
-
Linear & Multilinear Algebra . 2023, Vol. 71 Issue 16, p2645-2669. 25p. - Publication Year :
- 2023
-
Abstract
- Theory of numerical range and numerical radius for tensors is not studied much in the literature. Ke et al. [Linear Algebra Appl. 508 (2016), 100-132: MR3542984] introduced first the notion of the numerical range of a tensor via the k-mode product. However, the convexity of the numerical range via the k-mode product was not proved by them. In this paper, the notion of numerical range and numerical radius for even-order square tensors via the Einstein product are introduced first. Using the notion of the numerical radius of a tensor, we provide some sufficient conditions for a tensor to be 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR algebra
*TENSOR algebra
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 71
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 173436040
- Full Text :
- https://doi.org/10.1080/03081087.2022.2117771