Centrosymmetric matrix

In mathematics, especially in matrix theory, a centrosymmetric matrix is a matrix which is symmetric about its center. More precisely, an n x n matrix A = [ A_i,j ] is centrosymmetric if and only if its entries satisfy A_i,j = A_{n−i+1,n−j+1} for 1 ≤ i,j ≤ n.

2 x 2 centrosymmetric matrices have the form

${\begin{bmatrix}a&b\\b&a\end{bmatrix}}.$

3 x 3 centrosymmetric matrices have the form

${\begin{bmatrix}a&b&c\\d&e&d\\c&b&a\end{bmatrix}}.$

References

• T. Muir (1960), A Treatise on the Theory of Determinants, Dover, p. 19. ISBN 0-486-60670-8.

External links

• Centrosymmetric matrix on MathWorld.