Some Inequalities Of Hermite Non-Negative Definite Matrix

Recently, due to the development of mathematic and promotion of practices, the study of non-negative matrix have been become an important subject in the matrix research fields. Now, hermite non-negative definite matrix is topic problem.In this paper, we study the problem of inequalities for the trace and Hadamard product of hermite non-negative definite matrix.Our main work and results are summarized as follows.Firstly, the current study situation in the world about hermite non-negative definite matrix is introduced. After that we give some important concepts and explains some symbols;Secondly, in the basis of some scholars about several inequalities of hermite non-negative definite matrix trace. Further, several H older and Minkowski inequalities about the trace of hermite non-negative definite matrix are proposed according to the elementary inequalities and the method of matrix constant reform.Thirdly, we notice that, some theorems of hermite negative definite matrix are applied to hermite non-negative definite matrix.But, inequalities for Hadamard product of hermite negative definite matrix are not applicable to hermite non-negative definite matrix.In view of this, we introduce the Moore-Penrose inverse insteaded of a regular inverse.Finally, inequalities for Hadamard product of hermite non-negative definite matrix are given.