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Adjacency preserving maps on symmetric tensors.
- Source :
-
Linear Algebra & its Applications . Jun2024, Vol. 690, p27-58. 32p. - Publication Year :
- 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 ψ : 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYMMETRIC matrices
*INTEGERS
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 690
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 176465608
- Full Text :
- https://doi.org/10.1016/j.laa.2024.02.029