On Comon’s and Strassen’s Conjectures

Alex Casarotti, Alex Massarenti and Massimiliano Mella
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Alex Casarotti: Department of Mathematics and Informatics, University of Ferrara, 44121 Ferrara, Italy
Alex Massarenti: Department of Mathematics and Informatics, University of Ferrara, 44121 Ferrara, Italy
Massimiliano Mella: Department of Mathematics and Informatics, University of Ferrara, 44121 Ferrara, Italy

Mathematics, 2018, vol. 6, issue 11, 1-13

Abstract: Comon’s conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen’s conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition. We survey the main known results on these conjectures, and, under suitable bounds on the rank, we prove them, building on classical techniques used in the case of symmetric tensors, for mixed tensors. Finally, we improve the bound for Comon’s conjecture given by flattenings by producing new equations for secant varieties of Veronese and Segre varieties.

Keywords: Strassen’s conjecture; Comon’s conjecture; tensor decomposition; Waring decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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