Research of k-generalized Hermite matrix

The author stated concepts of k-generalized Hermite matrix,its properties and relations with Hermite matrix,unitary matrix,Hamilton matrix and generalized inverse matrix were discussed,with many new results obtained.The corresponding results among unitary matrix,Hermite matrix and generalized symmetric matrix,especially the Cayley decomposition of orthogonal matrix to k-generalized unitary matrix and k-generalized Hermite matrix were extended,and unifying various kinds of the Hermite matrix and generalized inverse matrix.