Coherence invariant maps on order-3 symmetric tensors
Document Type
Article
Publication Date
3-1-2024
Abstract
In 1940s, Hua established the fundamental theorems of geometry of rectangular matrices, symmetric matrices, skew-symmetric matrices, and hermitian matrices. In 1950s, Jacob generalized Hua's theorems to that of order-2 tensors and symmetric tensors. We extend Jacob's work to maps of order-3 symmetric tensors over C by proving that every surjective coherence invariant map on order-3 symmetric tensors over C is induced by a semilinear isomorphism apart from an additive constant.
Keywords
Symmetric tensors, Symmetric rank, Coherence invariant, Adjacency preserving
Divisions
MathematicalSciences
Funders
Ministry of Higher Education, Malaysia [Grant no. FRGS/1/2019/STG06/UM/02/1]
Publication Title
Linear and Multilinear Algebra
Volume
72
Issue
4
Publisher
Taylor and Francis Ltd.
Publisher Location
2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND