Abstract— In this paper, the anti-centrosymmetric matrices have been researched. According to the structural characteristics of the anti-centrosymmetric matrix, some new methods have been used to prove the necessary and sufficient conditions of a matrix being anti-centrosymmetric and its properties of eigenvalue and eigenvector; the nonsingularity of the anti-centrosymmetric matrices have been discussed,that the odd order anti-centrosymmetric matrix is singular has been obtained, and two methods of computing inverse of the matrices(even order) have been given.
Keywords— Anti-centrosymmetric Matrix, Centrosymmetric Matrix, Eigenvalue, Inverse Matrix.
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