Singular value decomposition for comb filter matrices

In this paper, we present an eigenvalue decomposition for any n×n complex matrix with constant diagonals Tn=(aj-k)j,k=1n satisfying that there exists a positive integer m such that ak=0 for all k∉{-m,0,m}. Moreover, from this eigenvalue decomposition we obtain a singular value decomposition for any...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 222; pp. 472 - 477
Main Author Gutiérrez-Gutiérrez, Jesús
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2013
Subjects
Computation
Decomposition
Eigenvalues
Eigenvectors
Integers
Mathematical analysis
Mathematical models
Matrices (mathematics)
Matrix methods
Pentadiagonal matrices
Singular values
Tridiagonal matrices
Tridiagonal matrices
Eigenvalues
Singular values
Eigenvectors
Pentadiagonal matrices
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Summary:In this paper, we present an eigenvalue decomposition for any n×n complex matrix with constant diagonals Tn=(aj-k)j,k=1n satisfying that there exists a positive integer m such that ak=0 for all k∉{-m,0,m}. Moreover, from this eigenvalue decomposition we obtain a singular value decomposition for any comb filter matrix.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.07.050