Abstract: The positive definiteness (semi-definiteness) matrix, t he generalized positive definiteness (semidefineteness) matrix, the generalized di agonally dominant matrix and M-matrix are widely used in the fi elds like autom atic control theory, neural network computing and robot, etc.. It is of great im portance to make criterion on them. Based on the existing criterion theorems, so me new criterion theorems which are more practical are given in this article.