二阶非负定阵的一些不等式

SOME INEQUALITIES FOR NON-NEGATIVE DEFINITE MATRICES OF ORDER 2

设A、B是二阶非负定阵,Γ_(s,t)={t_r(multiply from i=1 to (?)Gi)|G_i=A或B·s、t分别是乘积中A、B出现的次数}。对某些s和t,讨论了Γ_(s,t)上的偏序关系,得到了一些迹不等式。

Let A and B be 2×2 non-negative definite matrices, Γ_(s(?))={tr(multiply from i=1 to(s+(?))Gi): Gi=A or B; s, t are the numbers of times that A and B appear in the product respectively}. In this paper, we study the partial ordering on Γ_(s(?)). Some inequalities on traces are obtained.