两个正定Hermite矩阵间的一种半正定关系

Semi-positive Definite Relation Between Two Positive Definite Hermitian Matrixes

本文证明了两个交换ｎ阶正定Ｈｅｒｍｉｔｅ矩阵Ａ≥Ｂ的如下半正定Ｈｅｒｍｉｔｅ关系：１８（Ａ－Ｂ）２Ｂ－１≥１２（Ａ＋Ｂ）－（ＡＢ）１２≥１８（Ａ－Ｂ）２Ａ－１且等号成立的充要条件为Ａ＝Ｂ

Following semi-positive definite relation between tow exchangeable positive definite Hermitian matrixes A≥B of n order are proved:18(A-B) 2B -1 ≥12(A+B)-(A-B) 12 ≥18(A-B) 2A -1  Where necessary and sufficient condition for holding egual sign is A=B