Abstract
This paper is about linear transformations of the fc-fold symmetric tensor product of an ^-dimensional vector space V which carry nonzero decomposable tensors to nonzero decomposable tensors. The main theorem shows that every such transformation is induced by a nonsingular transformation of V provided both (i) the field has characteristic either 0 or a prime greater than k and every polynomial over the field with degree at n is a product of linear factors. (ii) n>k + l.
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