关于四元数矩阵迹的若干不等式

Some Inequalities on Traces of Quaternion Matrices

本文证明了关于四元数矩阵迹的一些不等式,它们是[5]、[6]的相应结果的推广。

In this paper some inequlities on traces of quaternion matrices are proved. They are some generalizations and improvements of[5]and[6]. Let Q^(m×n) denote the set of all m×n matrices over quaterion field. We have: 1 If A∈Q^2n×2n,A>0, A=A_1,A_2∈Q^(n×n), then(trA_1- nλ_(2n)(A))(trA_2-nλ_(2n)(A))≥(Re(trA_3))~2. 2 if A, B, C∈Q^(n×n), A>0,B≥C≥0, then Re[tr((A+B)^(-1)B)] ≥Re[tr((A+C)^(-1)C)]. 3 If A=A~*∈Q^(n×n),then sum from i=1 to k(λi(A))= tr uAu~*, sum from i=1 to k (λ) (A)=truA~*.