Abstract
Let V i {V_i} be a finite dimensional vector space over a field F for each i = 1 , 2 , … , m i = 1,2, \ldots ,m , and let z be a tensor in V 1 ⊗ ⋯ ⊗ V m {V_1} \otimes \cdots \otimes {V_m} . In this paper a set of homogeneous quadratic polynomials in the coordinates of z is exhibited for which the associated variety is the set of decomposable tensors. In addition, a question concerning the maximal tensor rank in such a situation is answered, and an application to other symmetry classes of tensors is cited.
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