Polynomial foldings and rank of tensors

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)173-206
Number of pages34
JournalJournal of Commutative Algebra
Volume8
Issue number2
DOIs
StatePublished - 2016

Keywords

  • Determinantal schemes
  • Multilinear algebra
  • Tensor rank

ASJC Scopus subject areas

  • Algebra and Number Theory

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