GENERABLZED UNITARY MATRICES AND GENERALIZED HERMITE MATRICES

The concepts of generalized unitary matrix and generalized (obilque)Hermite matrix are given, their properties and relations between they and unitary matrix, conjugate matrix,Hermite matris,Hamilton matrix and gereralized inverse matris are studied, and many new results are obtained. Moreover, the corresponding results on relations among unitary matrix,Hermite matrix and anit -Hermite matrix are popularized .especially the Cayley decomposition of orthogonal matrix is extended to generalized unitary matrix, and various kinds of the unitary matrix, Hermite matrix; generalized Hermite matrix and generalized inverse matrix unified.