A complete solution of the permutability problem for Toeplitz and Hankel matrices

Conditions under which two Toeplitz matrices commute are known since at least 1998. For a pair of Hankel matrices, the corresponding commutativity conditions were recently obtained by Gel'fgat. In this paper, we complete our analysis of the much more complex problem of characterizing matrix pai...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 478; pp. 53 - 80
Main Authors Chugunov, V.N., Ikramov, Kh.D.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2015
Subjects
Centrosymmetric matrix
Hankel matrix
Involution
Persymmetric matrix
Toeplitz matrix
Hankel matrix
15B05
Involution
Persymmetric matrix
Toeplitz matrix
Centrosymmetric matrix
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Summary:Conditions under which two Toeplitz matrices commute are known since at least 1998. For a pair of Hankel matrices, the corresponding commutativity conditions were recently obtained by Gel'fgat. In this paper, we complete our analysis of the much more complex problem of characterizing matrix pairs (T,H) such that T is a Toeplitz matrix, H is a Hankel matrix, and TH=HT. The only case left open in our previous publications on this subject is the one where the Toeplitz matrix T is centrosymmetric. Here, we present an exhaustive study of this case, which yields a complete solution of the above commutativity problem.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2015.03.010