文[1]推广了Bellman.R获得的正定矩阵A、B的迹的不等式:2tr(AB)≤tr(A^2)+tr(B^2)(*);tr(AB)≤[tr(A^2)]^(1╱2)·[tr(B^2)]^(1╱2)(**)。本文在两两相乘可交换的条件下给出更一般的不等式:tr(multiply from i=1 to m (A_i^(ai))≤s...文[1]推广了Bellman.R获得的正定矩阵A、B的迹的不等式:2tr(AB)≤tr(A^2)+tr(B^2)(*);tr(AB)≤[tr(A^2)]^(1╱2)·[tr(B^2)]^(1╱2)(**)。本文在两两相乘可交换的条件下给出更一般的不等式:tr(multiply from i=1 to m (A_i^(ai))≤sum from i=1 to m (a_i)·tr(A_i)(a_i〉0,sum from i=1 to m (a_i)=1);sum from 1-i to m(-tr) multiply from j=1 to k(A_(i-j))≤multiply from j=1 to k[sum from i=1 to m (tr(A_i^(β_i)]^(β^1)(β〉0,sum from j=1 to k(β=1))。展开更多
文摘文[1]推广了Bellman.R获得的正定矩阵A、B的迹的不等式:2tr(AB)≤tr(A^2)+tr(B^2)(*);tr(AB)≤[tr(A^2)]^(1╱2)·[tr(B^2)]^(1╱2)(**)。本文在两两相乘可交换的条件下给出更一般的不等式:tr(multiply from i=1 to m (A_i^(ai))≤sum from i=1 to m (a_i)·tr(A_i)(a_i〉0,sum from i=1 to m (a_i)=1);sum from 1-i to m(-tr) multiply from j=1 to k(A_(i-j))≤multiply from j=1 to k[sum from i=1 to m (tr(A_i^(β_i)]^(β^1)(β〉0,sum from j=1 to k(β=1))。