Archivio Istituzionale della RicercaLet H be a class of n × n Hankel matrices H_A whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field F_q. For every matrix in 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 F^n_q . 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.
On Determinantal Varieties of Hankel Matrices / Edoardo, Ballico; Elia, Michele. - In: ALGEBRA. - ISSN 2314-4106. - ELETTRONICO. - 2014:(2014). [10.1155/2014/970157]
On Determinantal Varieties of Hankel Matrices
ELIA, Michele
2014
Abstract
Let H be a class of n × n Hankel matrices H_A whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field F_q. For every matrix in 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 F^n_q . 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.
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https://hdl.handle.net/11583/2542309
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