Inflation matrices and ZME-matrices that commute with a permutation matrix

Centrosymmetric matrices are matrices that commute with the permutation matrix $J$, the matrix with ones on its cross-diagonal. This paper generalizes the concept of centrosymmetry, and considers the properties of matrices that commute with an arbitrary permutation matrix $P$, the $P$-commutative ma...

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Bibliographic Details
Published inSIAM journal on matrix analysis and applications Vol. 9; no. 3; pp. 408 - 418
Main Author STUART, J. L
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.07.1988
Subjects
Eigenvalues
Eigenvectors
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Characterization
Mathematical matrix
Generalization
Symmetric matrix
Permutation
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Summary:Centrosymmetric matrices are matrices that commute with the permutation matrix $J$, the matrix with ones on its cross-diagonal. This paper generalizes the concept of centrosymmetry, and considers the properties of matrices that commute with an arbitrary permutation matrix $P$, the $P$-commutative matrices. In particular,it focuses on two related classes of matrices: inflation matrices and $ZME$-matrices. The structure of $P$-commutative inflators is determined, and then this is used to characterize the $P$-commutative $ZME$-matrices. Centrosymmetric matrices in these classes are presented as a special case.
ISSN:0895-4798
1095-7162
DOI:10.1137/0609036