Abstract
A natural group action on a three-tensor is considered in a special case where one of the vector spaces is two-dimensional. We are concerned with finding a complete set of invariants under this group action. Kronecker’s theory of pencils is viewed as giving a solution to this problem in the case of a smaller group action. In this paper we extend these results to get a complete set of invariants under the larger and more natural group action. This has direct implications on a problem in computational complexity: that of the optimal evaluation of a pair of bilinear forms.
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