- Bisymmetric matrix
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 and only if it satisfies "A = AT" and "AJ = JA" where "J" is the "n" × "n"exchange matrix .Properties
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 matrixcite journal | last = Tao | first = D. | coauthors = Yasuda, M. | title = A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew-centrosymmetric matrices | journal = SIAM J. Matrix Anal. Appl. | volume = 23 | issue = 3 | pages = 885–895 | date = 2002 | url = http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJMAEL000023000003000885000001&idtype=cvips&gifs=Yes
accessdate = 2007-10-12 | doi = 10.1137/S0895479801386730] .References
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