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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| 格式: | Article |
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Elsevier
2024
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| 在線閱讀: | http://eprints.um.edu.my/45418/ https://doi.org/10.1016/j.laa.2024.02.029 |
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| 總結: | 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. |
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