摘要
本文将矩阵迹的Ｂｅｌｍａｎ不等式加以推广，证得：ｔｒ（ＡＢ）２ｍ≤ｍｉｎ｛〔ｔｒ（ＡＢ）〕２ｍ，ｔｒ（Ａ２ｍＢ２ｍ）｝；ｍａｘ｛〔ｔｒ（ＡＢ）〕２。
Bellman's inequalities for the matrix trace are spread in the paper. we have proved tr(AB)2m≤min{〔tr(AB)〕2m,tr(A2mB2m)} and max{〔tr(AB)〕2,tr(A2B2)}≤tr(A2)tr(B2)
关键词
实正定对称矩阵
非负定矩阵
广义实正定矩阵
矩阵迹
BELLMAN不等式
real positive definite symmetric matrix, semi-positive definite matrix, generalized real positive matrix, inequalities.
