Several Of The Inverse M-matrix And Of Khatri-rao Product Of Inequality

Special matrices Play important roles in matrix analysis and matrix computation and have wide applications in computational mathematics, applied mathematics, economics, physics, biology and etc. The special matrices included inverse M-matrices, inverse Z-matrices, tridiagonal matrices and nonnegative irreducible matrices. This thesis presents a systematic research on some types of special matrices such as inverse M-matrices. It is shown in thesis that nonnegative matrices whose inverses are M-matrices. And we obtained some special matrices in researches on inverse M-matrices. And we presents some properties of inverse M-matrices, tridiagonal matrices. This thesis Presents a systematic research on some special algorithm of matrices such as Khatri-Rao products, Tracy-singh products, Hadamard product and Kronecker products.The thesis consists of two parts. In the part one, we generalize a class of type-Z) matrices which has some properties of inverse Z -matrices, inverse L_s -matrices. And we defined a new class of generalized type-D matrices that has analogous properties. A class of generalized type-Z) matrices is investigated and some properties of inverse Z -matrices, inverse L_s -matrices, inverse M-matrices and diagonally dominant matrices are presented. And we study of some properties of inverse M-matrices, tridiagonal matrices.In the part two, several inequalities involving Khatri-Rao and Tracy-singh products of positive semidefinite matrices are investigated. A further study of the Khatri-Rao products for positive semi-definite matrice is made. Some inequalities involving the Khatri-Rao products, Tracy-singh product, Hadamard products and Kronecker products of several matrices are presented. And some inequalities involving the Khatri-Rao, Hadamard and Kronecker products are presented.