Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

Subjects:
Primary: 13C40, 14M12, 15A69

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.8 • No. 2 • 2016
Back to Top