About two trigonometric matrices
type: Item
instance of: scholarly article
title: About two trigonometric matrices
zbMATH Open document ID: 1053.15019
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
full work available at URL: http://hdl.handle.net/2434/6853
review text: The author studies the four matrices \[ M_{r,s} : =\sqrt{2}\left[ \sin \left(\pi {rmn}/{s}\right)\right] _{0<m,n<s},M_{2r,s}:=\sqrt{2}\left[ \sin \left( {2}\pi {rmn}/{s} \right) \right] _{0<m,n<s}, \] \[ M_{r,s}^{\prime } : =\sqrt{2}\left[ \sin \left( \pi{rmn}/{s} \right) \right] _{\substack{ 0<m,n<s\\ ( mn,s) =1}},M_{2r,s}^{\prime }:=\sqrt{2}\left[ \sin \left( {2}\pi{rmn}/{s} \right) \right] _{\substack{ 0<m,n<s\\ ( mn,s) =1}}, \] where \(r,s\) are odd integers with \(( r,s) =1\) and \(s>1\). More specifically the paper determines the eigenvalues of the above matrices and their multiplicities, as well as their characteristic polynomials.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 2081901
zbMATH Keywords: trigonometric matrices
zbMATH Keywords: Dirichlet characters
zbMATH Keywords: eigenvalues
zbMATH Keywords: characteristic polynomials
author: Giuseppe Molteni
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
OpenAlex ID: W2016722805
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DOI: 10.1016/J.LAA.2003.12.016
description: scientific article; zbMATH DE number 2081901