On The Positive Definiteness Of Matrices

The positive definiteness of matrix is an important conception of matrix theory.This dissertation mainly discuss the positive definiteness of the matrices that are not necessarily symmetric,and further extend the definition of positive definite matrices .There are two chapters in this dissertation.In the first chapter,We give the definition of positive definiteness of general matrices,and extend some results of positive definite symmetric matrices.Then we obtain several sufficient and necessary conditions about positive definiteness of matrices.We study characteristic value and main sub-determinant of positive definite matrices.Finally we study positive definiteness of product of matrices . In the second chapter,we mainly discuss the generalized positive definite matrices,obtain several description and decision of the generalized positive definite matrices.Simultaneously we extend the definition of the generalized positive definite matrices ,At the end of this dissertation ,we give several simple propositions about the generalized positive definite matrices,the we explain them by some examples.