Centrosymmetric matrix

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This article defines a property that can be evaluated for a square matrix. In other words, given a square matrix (a matrix with an equal number of rows and columns) the matrix either satisfies or does not satisfy the property.
View other properties of square matrices


Verbal definition

A centrosymmetric matrix is a square matrix that commutes with the exchange matrix (the matrix with 1s on the antidiagonal and 0s elsewhere) of the same number of rows and columns.

Algebraic definition

Suppose is a positive integer. A matrix is termed a centrosymmetric matrix if it satisfies the following condition:

In symbols, if denotes the exchange matrix, then is centrosymmetric if and only if .

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
symmetric Toeplitz matrix Bisymmetric matrix|FULL LIST, MORE INFO
bisymmetric matrix centrosymmetric and a symmetric matrix |