The paper has discussed such problims as the properties of sub-eigenvalue and sub-eigenvector of real-anti-sub-symmetric matrix

and its diagonalization.Based on the above

the following result could be approached:If Ais a realanti-sub-symmetric matrix

then there exists a perpendicular matrix P.Multiplied with P and its reversal PSTfrom the right and the left respectively

the matrix will become a diagonalmatrix.