Adjacency preserving maps on symmetric tensors
Document Type
Article
Publication Date
6-1-2024
Abstract
Let r and s be positive integers such that r 2. Let U and V be vector spaces over fields F and K, respectively, such that dim U 3 and F has at least r + 1 elements. In this paper, we characterize surjective maps psi : S r U -> S s V preserving adjacency in both directions on symmetric tensors of finite order, which generalizes Hua's fundamental theorem of geometry of symmetric matrices. We give examples showing the indispensability of the assumptions dim U 3 and the cardinality | F| r + 1 in our result. (c) 2024 Published by Elsevier Inc.
Keywords
Adjacency preserving map, Symmetric tensor, Symmetric 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
690
Publisher
Elsevier
Publisher Location
STE 800, 230 PARK AVE, NEW YORK, NY 10169 USA