Hyperdeterminant

A technically defined extension of the ordinary Determinant to ``higher dimensional''Cayley (1845) originally coined the term, but subsequently used it to refer to anAlgebraic Invariant of a multilinear form. The hyperdeterminant of the Hypermatrix (for , 1) is given by

The above hyperdeterminant vanishes Iff the following system of equations in six unknowns has a nontrivial solution,

References

Cayley, A. ``On the Theory of Linear Transformations.'' Cambridge Math. J. 4, 193-209, 1845.

Gel'fand, I. M.; Kapranov, M. M.; and Zelevinsky, A. V. ``Hyperdeterminants.'' Adv. Math. 96, 226-263, 1992.

Schläfli, L. ``Über die Resultante eine Systemes mehrerer algebraischer Gleichungen.'' Denkschr. Kaiserl. Akad. Wiss., Math.-Naturwiss. Klasse 4, 1852.

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