Study on Some Properties of Anti-centrosymmetric Matrices

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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Dynamic analyses of a flat plate and a beam subjected to a moving load

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