Several Properties of the Generalized Positive Definite Complex Matrix

Positive definite complex matrix is an important concept of the matrix theory,several properties and structures of which have been comprehended.When the concept of the generalized positive definite complex matrix is introduced,we should also discuss corresponding properties and structures which are undoubtedly meaningful to enrich the content of the matrix theory.This paper discusses some relevant facts of the generalized positive definite complex matrix on the basis of the positive definite complex matrix,provides six equivalent definitions of the generalized positive definite complex matrix,three properties and four inequalities for the generalized positive definite complex matrix determinant or its mold.