Tensor ranks and symmetric tensor ranks are the same for points with low symmetric tensor rank |
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Authors: | E Ballico |
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Institution: | 1.Dept. of Mathematics,University of Trento,Povo,Italy |
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Abstract: | Fix integers n ≥ 1, d ≥ 2. Let V be an (n + 1)-dimensional vector space over a field with characteristic zero. Fix a symmetric tensor \({T\in S^d(V)\subset V^{\otimes d}}\). Here we prove that the tensor rank of T is equal to its symmetric tensor rank if the latter is at most (d + 1)/2. |
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