Abstract:

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.

Key words: k-generalized Hermite matrix, unitary matrix;  generalized inverse matrix； symplectic matrix； matrix equation