Adjacency preserving maps on symmetric tensors

Adjacency preserving maps on symmetric tensors

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...

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Main Authors: Chooi, Wai Leong, Lau, Jinting
Format: Article
Published: Elsevier 2024
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QA Mathematics
Online Access:http://eprints.um.edu.my/45418/
https://doi.org/10.1016/j.laa.2024.02.029
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Institution: Universiti Malaya
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spelling my.um.eprints.454182024-10-21T04:31:03Z http://eprints.um.edu.my/45418/ Adjacency preserving maps on symmetric tensors Chooi, Wai Leong Lau, Jinting QA Mathematics 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. Elsevier 2024-06 Article PeerReviewed Chooi, Wai Leong and Lau, Jinting (2024) Adjacency preserving maps on symmetric tensors. Linear Algebra and its Applications, 690. pp. 27-58. ISSN 0024-3795, DOI https://doi.org/10.1016/j.laa.2024.02.029 <https://doi.org/10.1016/j.laa.2024.02.029>. https://doi.org/10.1016/j.laa.2024.02.029 10.1016/j.laa.2024.02.029
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Chooi, Wai Leong
Lau, Jinting
Adjacency preserving maps on symmetric tensors
description 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.
format Article
author Chooi, Wai Leong
Lau, Jinting
author_facet Chooi, Wai Leong
Lau, Jinting
author_sort Chooi, Wai Leong
title Adjacency preserving maps on symmetric tensors
title_short Adjacency preserving maps on symmetric tensors
title_full Adjacency preserving maps on symmetric tensors
title_fullStr Adjacency preserving maps on symmetric tensors
title_full_unstemmed Adjacency preserving maps on symmetric tensors
title_sort adjacency preserving maps on symmetric tensors
publisher Elsevier
publishDate 2024
url http://eprints.um.edu.my/45418/
https://doi.org/10.1016/j.laa.2024.02.029
_version_ 1814047556475289600

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