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.
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