Computing symmetric rank for symmetric tensors

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Abstract

We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2×⋯×2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.

Keywords

Symmetric tensor
Tensor rank
Secant variety

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This research was partly supported by MIUR and RFO of Univ. of Bologna, Italy, CIRM–FBK Trento, Italy.

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