A complete solution of the normal Hankel problem
type: Item
instance of: scholarly article
title: A complete solution of the normal Hankel problem
zbMATH Open document ID: 1194.15027
published in: Linear Algebra and its Applications
publication date: 2010-05-11T00:00:00Z
review text: The object of the paper is to characterize the \(n\times n\) Hankel matrices which are normal. If \(P_{n}\) is the \(n\times n\) matrix whose \((i,j)\)-th entry is \(1\) if \(i+j=n+1\) and \(0\) otherwise (the ``backward identity'' matrix) and \(H\) is Hankel then \(T:=HP_{n}\) is Toeplitz. It is easily seen that \(H\) is normal if and only if \(TT^{\ast}\) is real. Equivalently, writing \(T=T_{1}+iT_{2}\) where \(T_{1}\) and \(T_{2}\) are real, the Hankel matrix \(H\;\)is normal if and only if \(T_{1}T_{2}^{t} =T_{2}T_{1}^{t}\). Using a case-by-case analysis the authors determine the \(T\) for which \(H=TP_{n}\) is normal Hankel.
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5706978
zbMATH Keywords: Hankel matrix
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: circulant
zbMATH Keywords: normal matrix
zbMATH Keywords: backward identity
author: V. N. Chugunov
author: Kh. D. Ikramov
MaRDI profile type: Publication
full work available at URL: j.laa.2010.01.021
OpenAlex ID: W2094100663
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DOI: 10.1016/J.LAA.2010.01.021
description: scientific article; zbMATH DE number 5706978