Vol. 42, No. 3, 1972

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Transformations of symmetric tensors

Larry Jean Cummings

Vol. 42 (1972), No. 3, 603–613
Abstract

This paper is about linear transformations of the k-fold symmetric tensor product of an n-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 + 1.

Mathematical Subject Classification 2000
Primary: 15A72
Milestones
Received: 10 June 1971
Revised: 22 October 1971
Published: 1 September 1972
Authors
Larry Jean Cummings