Adjacency preserving maps between tensor spaces
Document Type
Article
Publication Date
8-1-2024
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.
Keywords
Adjacency preserving map, Tensor, Tensor rank, Geometry of matrices
Divisions
MathematicalSciences
Funders
Ministry of Higher Education, Malaysia (MOHE) via Fundamental Research Grant Scheme (FRGS/1/2022/STG06/UM/02/7)
Publication Title
Linear Algebra and its Applications
Volume
694
Publisher
Elsevier
Publisher Location
STE 800, 230 PARK AVE, NEW YORK, NY 10169 USA