Singular hypersurfaces and multilinear algebra
type: Item
instance of: scholarly article
title: Singular hypersurfaces and multilinear algebra
zbMATH Open document ID: 0953.15012
DOI: 10.1007/BF02169158
author: V. V. Dolotin
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-11-22T00:00:00Z
review text: The paper investigates determinants of multidimensional matrices and a multidimensional eigenvalue theory. The author shows how the invariants of n-ary forms can be produced from the discriminants of multilinear forms (determinants of multidimensional matrices), which should be considered as a generalization of the classical Hessians and resultants, and develops a technique which gives an algorithm for calculating the discriminants of multilinear forms. He establishes the degeneracy of a \(d\)-linear form in terms of the structure of the set of critical points of the corresponding homogeneous polynomial function. Finally, the example of 3-linear forms is illustrated.
reviewed by: M. Ladra
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14Q10
zbMATH DE Number: 1364730
zbMATH Keywords: rectangular matrices
zbMATH Keywords: multilinear forms
zbMATH Keywords: discriminants
zbMATH Keywords: determinants
zbMATH Keywords: singular hypersurfaces
zbMATH Keywords: determinants of multidimensional matrices
zbMATH Keywords: multidimensional eigenvalue
zbMATH Keywords: Hessians
zbMATH Keywords: resultants
zbMATH Keywords: algorithm
zbMATH Keywords: degeneracy
MaRDI profile type: Publication
cites work: Invariant Theory
full work available at URL: https://doi.org/10.1007/bf02169158
OpenAlex ID: W2042761858
description: scientific article; zbMATH DE number 1364730