Several Inequalities of the Matrix Trace Based on Hadamard Product
Xue Lan-lan · 2012
In this paper,we get Bellman type,Young type and other inequalities based on the Hadamard product.The main conclusions are as follows: Bellman type inequality,Suppose A,B∈Hn×n≥0,n is positive integer,then tr(A。B)n=tr(An。Bn)≤trAn·trBn≤(trA)n·(trB)n;Young type inequality,Suppose A,B∈Hn×n≥0,p1,q1,1/p+1/q=1,then tr(A。B)≤1/ptrAp+1/qtrBq.