Open Access
2016 Polynomial foldings and rank of tensors
Steven P. Diaz, Adam Lutoborski
J. Commut. Algebra 8(2): 173-206 (2016). DOI: 10.1216/JCA-2016-8-2-173


We review facts about rank, multilinear rank, multiplex rank and generic rank of tensors as well as folding of a tensor into a matrix of multihomogeneous polynomials. We define the new concept of folding rank of tensors and compare its properties to other ranks. We review the concept of determinantal schemes associated to a tensor. Then we define the new concept of a folding generic tensor meaning that all its determinantal schemes behave generically. Our main theorem states that for ``small'' 3-tensors, any folding generic tensor has generic rank, and the reverse does not always hold.


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Steven P. Diaz. Adam Lutoborski. "Polynomial foldings and rank of tensors." J. Commut. Algebra 8 (2) 173 - 206, 2016.


Published: 2016
First available in Project Euclid: 10 June 2016

zbMATH: 1360.13030
MathSciNet: MR3510917
Digital Object Identifier: 10.1216/JCA-2016-8-2-173

Primary: 13C40 , 14M12 , 15A69

Keywords: determinantal schemes , multilinear algebra , tensor rank

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.8 • No. 2 • 2016
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