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


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].


Spectral Sequence Matrix Entry Boundary Format Elementary Symmetric Polynomial Multilinear Form 
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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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