Adjacency preserving maps on symmetric tensors

• المؤلفون الرئيسيون: Chooi, Wai Leong, Lau, Jinting
• التنسيق: مقال
• منشور في: Elsevier 2024
• الموضوعات: QA Mathematics
• الوصول للمادة أونلاين: http://eprints.um.edu.my/45418/; https://doi.org/10.1016/j.laa.2024.02.029

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.