On apolarity and generic canonical forms

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14 Scopus citations


The notion of S-algebra is introduced. The theory of apolarity and generic canonical forms for polynomials is generalized to S-algebras over the complex field C. We apply this theory to the problem of finding the essential rank of general, symmetric, and skew-symmetric tensors. Upper bounds for the essential ranks are found by different combinatorial coverings.

Original languageEnglish
Pages (from-to)167-194
Number of pages28
JournalJournal of Algebra
Issue number1
StatePublished - Mar 1 1999

ASJC Scopus subject areas

  • Algebra and Number Theory


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