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Hyperdeterminants

  • Israel M. Gelfand
  • Mikhail M. Kapranov
  • Andrei V. Zelevinsky
Part of the Mathematics: Theory & Applications book series (MBC)

Abstract

The goal of this chapter is to provide a natural “higher dimensional” generalization of the classical notion of the determinant of a square matrix. There were some attempts toward a rather straightforward definition of the “hyperdeterminant” for “hypercubic” matrices using alternating summations over the product of several symmetric groups (see e.g., [P], §54 and references therein). Here we systematically develop another approach under which the hyperdeterminant becomes a special case of the general discriminant studied in the previous chapters. As so many other ideas in the field, this approach is due to Cayley [Ca1].

Keywords

Spectral Sequence Matrix Entry Boundary Format Elementary Symmetric Polynomial Multilinear Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Israel M. Gelfand
    • 1
  • Mikhail M. Kapranov
    • 2
  • Andrei V. Zelevinsky
    • 3
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsNortheastern UniversityBostonUSA

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