Chooi, Wai Leong and Lau, Jinting and Lim, Ming Huat (2024) Adjacency preserving maps between tensor spaces. Linear Algebra and its Applications, 694. pp. 307-334. ISSN 0024-3795, DOI https://doi.org/10.1016/j.laa.2024.04.018.
Full text not available from this repository.Abstract
Let r and s be positive integers such that r 3. Let U 1 , ... , U r be vector spaces over a field F and V 1 , ... , V s be vector spaces over a field K such that dim Uz, z , dim V j >= 2 for all i, j . In this paper, we characterize maps psi : circle times rz =1 U z -> circle times sz =1 V z that preserve adjacency in both directions, which extends Hua's fundamental theorem of geometry of rectangular matrices. We also characterize related results concerning locally full maps preserving adjacency in both directions between tensor spaces, maps preserving adjacency in both directions between tensor spaces over a field all whose nonzero endomorphisms are automorphisms, and injective continuous adjacency preserving maps on finite dimensional tensor spaces over the real field. (c) 2024 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Funders: | Ministry of Higher Education, Malaysia (MOHE) via Fundamental Research Grant Scheme (FRGS/1/2022/STG06/UM/02/7) |
| Uncontrolled Keywords: | Adjacency preserving map; Tensor; Tensor rank; Geometry of matrices |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 09 Apr 2025 04:34 |
| Last Modified: | 09 Apr 2025 04:34 |
| URI: | http://eprints.um.edu.my/id/eprint/46724 |
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