With regard to the value and difficulty of research on matrices over skew field,Professor Xie Bangjie s research on matrix similarity canonical form,weak canonical form descriptive theorem,eigenvalue basis of centerable matrices,determinant program and self-conjugate quaternionic matrices over skew field in 1978～1982 are reviewed.

In this paper,the new method is presented to determine the number of hidden nodes of RBF neural networks,it makes use of the whole inputting and outputting information of training samples to establish similar matrix of samples,then to determine the number of hidden nodes of RBF neural networks by maximal matrix element method.

By computing the power of Jordan matrix and the theory of similar matrix,the analytic formulation of the general solution of the constant coefficient homogeneous linear difference equation is presented.

Fuzzy clustering is associated with comprehensive assessment in the study of sorting when the number of object is large,and we improve the method of setting up fuzzy similar matrix.

Relation in characteristic vectors of similar matrices;

In this method,by computing the fuzzy similar matrices and transitive closure,fuzzy cluster is done with.

Based on from the fact that similar matrices have the same polynomial,we change and weaken concerned conditions in the propersition then get conclusions about charactersitc polynomials of matrices.