Some Inequalities for Positive Definite Hermitian Matrices

This paper generalizes some inequalities given in and ,and gets the following results:(1)If A1,A2,...,Ak are positive definite or positive semidefinite Hermitian matrices of order n,and p1n,|A1+...+Ak|p|A1|+...+|Ak|p;(2)If all Ai,Bi,...,Ci(i=1,...,k)are positive definite or positive semidefinite Hermitian matrices of order n,α0,β0,...,r0,and α+β+...+r1n,then ∑ki=1|Ai|α*|Bi|β...|Ci|r|∑ki=1Ai|α*|∑ki=1Bi|β...|∑ki=1Ci|r.