Some Properties of Generalized Unitary Matrices and Generalized Hermite Matrices

This paper focuses on two types of special matrices: the generalized unitary matrix and the generalized Hermite matrix.Promoted the nature of these two types of matrices we can obtained several new conditions of these two types of matrices.Such as: if a matrix A∈Cnn similar to a unitary matrix U,then A is the n-generaliized unitary matrix;if A can be diagonallyzable,then A is a n-generalized unitary matrix the necessary and sufficient condition is A similar to a unitary matrix;if A is a generalized P-unitary matrix,then A is a generalized P*-unitary matrix;if a matrix A is a real matrix,then A is a generalized Hermite matrix;if A is a n-order generalized P-Hermite matrix,then A is a n-order generalized P*-Hermite matrix.Gives the eigenvalues of the generalized unitary matrices: if λ≠0 is the eigenvalues of A,then 1λ is the eigenvalues of A*;when A is a real matrix,1λ is the eigenvalues of A.