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

Publication Title

Linear and Multilinear Algebra

Divisions

MathematicalSciences

Funders

Ministry of Higher Education, Malaysia [Grant no. FRGS/1/2019/STG06/UM/02/1]

Volume

72

Issue

4

Publisher

Taylor and Francis Ltd.

Publisher Location

2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND

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