Introduzione all'iperdeterminante
La Matematica nella società e nella cultura, Série 1, Tome 5 (2012) no. 2, pp. 169-195
Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica
The hyperdeterminant is one of the natural generalizations of the determinant to ``hypercubic'' matrices, it was introduced by Cayley in 1845. We describe how some properties of the determinant extend to the multidimensional setting. The starting point is the condition for the existence of nontrivial solutions to a square homogeneous linear system, which is given by the vanishing of the determinant. In the multidimensional case, the conditions for the existence of nontrivial solutions to a multilinear system allow to define the boundary format case, where there is a well defined diagonal. From the geometric perspective, the hyperdeterminant is defined through the dual varieties. We study the behaviour of the determinant after swapping two ``slices'' and its multiplicative properties.
@article{RIUMI_2012_1_5_2_a2,
author = {Ottaviani, Giorgio},
title = {Introduzione all'iperdeterminante},
journal = {La Matematica nella societ\`a e nella cultura},
pages = {169--195},
year = {2012},
volume = {Ser. 1, 5},
number = {2},
zbl = {1391.15022},
mrnumber = {3059949},
language = {it},
url = {http://geodesic.mathdoc.fr/item/RIUMI_2012_1_5_2_a2/}
}
Ottaviani, Giorgio. Introduzione all'iperdeterminante. La Matematica nella società e nella cultura, Série 1, Tome 5 (2012) no. 2, pp. 169-195. http://geodesic.mathdoc.fr/item/RIUMI_2012_1_5_2_a2/