Positive Definite Matrix And Positive Definite Matrix Inequality

Positive definite matrix plays a very important role in the matrix theory. In thispaper, it studied in the properties of positive definite matrix and the inequality ofpositive definite matrix, and discussed some of its applications. Firstly, it discussed thereal positive definite matrix, the properties of positive definite matrix and the equivalentproposition. Then, some inequalities of the theory of real number were generalized topositive definite matrix. It received some Hilbert-Schmidt norm of positive definitematrix of Young inequality and Heinz inequality, and also improved the Holder type ofmatrix inequalities. Finally, positive definite matrix was expounded in the concreteapplication of mathematical statistics, physics, etc.