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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| Published in | SIAM journal on matrix analysis and applications Vol. 9; no. 3; pp. 408 - 418 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.07.1988
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | STUART, J. L |
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| Cites_doi | 10.2307/3212257 10.2307/2323222 10.1080/00401706.1970.10488743 |
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| Copyright | 1989 INIST-CNRS [Copyright] © 1988 © Society for Industrial and Applied Mathematics |
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| DOI | 10.1137/0609036 |
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| Keywords | Characterization Mathematical matrix Generalization Symmetric matrix Permutation |
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| References | Friedland Shmuel (R1) 1987; 300 R3 R4 R6 Gantmacher F. R. (R2) 1959 Lancaster Peter (R5) 1969 |
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| Snippet | Centrosymmetric matrices are matrices that commute with the permutation matrix $J$, the matrix with ones on its cross-diagonal. This paper generalizes the... |
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| SubjectTerms | Eigenvalues Eigenvectors Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use |
| Title | Inflation matrices and ZME-matrices that commute with a permutation matrix |
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