scholarly journals Skew-symmetric tensor decomposition

2019 ◽  
pp. 1950061
Author(s):  
Enrique Arrondo ◽  
Alessandra Bernardi ◽  
Pedro Macias Marques ◽  
Bernard Mourrain
Keyword(s):  
Tensor Decomposition ◽  
Symmetric Tensor ◽  
Minimal Decomposition ◽  
New Algorithms

We introduce the “skew apolarity lemma” and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in [Formula: see text] with [Formula: see text] and [Formula: see text]. New algorithms to compute the rank and a minimal decomposition of a tritensor are also presented.

scholarly journals Symmetric tensor decomposition

2010 ◽  
Vol 433 (11-12) ◽  
pp. 1851-1872 ◽  
Author(s):  
Jerome Brachat ◽  
Pierre Comon ◽  
Bernard Mourrain ◽  
Elias Tsigaridas
Keyword(s):  
Tensor Decomposition ◽  
Symmetric Tensor

scholarly journals On Comon’s and Strassen’s Conjectures

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 217 ◽  
Author(s):  
Alex Casarotti ◽  
Alex Massarenti ◽  
Massimiliano Mella
Keyword(s):  
Tensor Decomposition ◽  
Symmetric Tensor ◽  
Symmetric Tensors ◽  
Secant Varieties ◽  
Segre Varieties

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.

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