On determinantal varieties of Hankel matrices
type: Item
instance of: scholarly article
title: On determinantal varieties of Hankel matrices
zbMATH Open document ID: 1327.14216
DOI: 10.1155/2014/970157
author: E. Ballico
author: Michele Elia
published in: Algebra
publication date: 2015-12-11T00:00:00Z
review text: Summary: Let \(\mathfrak H\) be a class of \(n\times n\) Hankel matrices \(\mathbf{H}_A\) whose entries, depending on a given matrix \(\mathbf A\), are linear forms in \(n\) variables with coefficients in a finite field \(\mathbb F_q\). For every matrix in \(\mathfrak H\), it is shown that the varieties specified by the leading minors of orders from 1 to \(n-1\) have the same number \(q^{n-1}\) of points in \(\mathbb F_q^n\). Further properties are derived, which show that sets of varieties, tied to a given Hankel matrix, resemble a set of hyperplanes as regards the number of points of their intersections.
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 6519802
Wikidata QID: Q59052685
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/970157
OpenAlex ID: W2119036256
cites work: Determinantal hypersurfaces.
cites work: Q3539736
cites work: Q5609066
cites work: Analysis of one-dimensional linear hybrid cellular automata over GF(q)
cites work: On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field
cites work: A simple derivation of the Berlekamp- Massey algorithm and some applications (Corresp.)
description: scientific article; zbMATH DE number 6519802