k-Generalized Hermite Matrices and Their Application in Matrix Equation

The concept of k-generalized Hermite matrix was given,and its properties and relations to unitary matrix,Hermite matrix,Hamilton matrix and generalized inverse matrix,and its matrix equation of application were discussed,with many new results obtained.The corresponding results of 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,unifying various kinds of Hermite matrix and generalized inverse matrix.