Hyperdeterminants
type: Item
instance of: scholarly article
title: Hyperdeterminants
zbMATH Open document ID: 0774.15002
DOI: 10.1016/0001-8708(92)90056-Q
author: Mikhail Kapranov
author: I. M. Gel'fand
author: Andrei Zelevinsky
published in: Advances in Mathematics
publication date: 1993-06-29T00:00:00Z
review text: Take \(A\) a square matrix \(n\times n\), it is well known that the determinant is a homogeneous polynomial in the coefficients of the matrix. Now consider a hypercubic matrix \(n_ 1\times n_ 2\times\cdots\times n_ k\), is it possible to define the determinant in this case? Using Projective Algebraic Geometry the authors can define the hyperdeterminant of this hypercubic matrix. It is a polynomial if some conditions on \(n_ 1,n_ 2,\dots,n_ k\) are given. Some properties of the hyperdeterminant are studied but there are many open problems in this new theory.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 221236
zbMATH Keywords: hypercubic matrix
zbMATH Keywords: hyperdeterminant
reviewed by: Marcel Morales
MaRDI profile type: Publication
cites work: Q3347989
cites work: The analysis of elliptic families. I: Metrics and connections on determinant bundles
cites work: Q4711942
cites work: Q3202241
cites work: Q4195061
cites work: Q3995279
cites work: Chow polytopes and general resultants
cites work: Duale Varietäten von Fahnenvarietäten. (Dual varieties of flag varieties)
cites work: Q3947818
cites work: Vector bundles on complex projective spaces
cites work: Q3851094
cites work: Q3994886
cites work: Q5837360
full work available at URL: 0001-8708(92)90056-q
OpenAlex ID: W4210751313
description: scientific article; zbMATH DE number 221236