In mathematics, a bisymmetric matrix is a square matrix that is symmetric about both of its main diagonals. More precisely, an n × n matrix A is bisymmetric if it satisfies both A = AT and AJ = JA where J is the n × n exchange matrix.
Bisymmetric matrices are both symmetric centrosymmetric and symmetric persymmetric. It has been shown that real-valued bisymmetric matrices are precisely those symmetric matrices whose eigenvalues are the same up to sign after pre or post multiplication by the exchange matrix.
The product of two bisymmetric matrices results in a centrosymmetric matrix
- Tao, D.; Yasuda, M. (2002). "A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew-centrosymmetric matrices". SIAM J. Matrix Anal. Appl. 23 (3): 885–895. doi:10.1137/S0895479801386730. Retrieved 2007-10-12.