On The Spectral Radius Of Non-negative Matrix And The Hermitian Matrix Inequality

We study the special matrix inequalities,which are spectral radius inequalities of nonnective matrices,the inequalities of matrix exponentials and the inequalities invoving Khatri-Rao sums.this paper contains four chapters:In chapter 1,we introduce some properties and some theorems which are to be used in this paper.In chapter 2, the comparison of the spectral radius of the nonnegative matrices is transformed to the comparison of the size of the elements of nonnegative ma-trices through integrating the elements of matrices with the spectral radius of the nonnegative matrices,by applying the method of analysising of the elements of the matrices.The size of the spectral radius of the nonnegative matrices and the positive semidefinite nonnegative matrices are researched by using this method.In chapter 3, it mainly promoted some results of matrix exponentials about Kronecker products(sums),Khatri-Rao products(sums),Tracy-Singh product(sums), commutators of matrix and so on,then it got some new properties of matrix expo-nentials and it's equalities and inequalities.In chapter 4.using a special matrix inequalities,the Khatri-Rao sums of positive semidefinite matrix and the sums of hermitian matrix were have been made a further research,then it got some inequalities involving the Khatri-Rao sums.