Rellman猜想在四元数体的修正

CORRECTION TO BELLMAN CONJECTURE OVER QUATERNION FIELD

本文就ｎ＝２￣ｔ（ｔ为自然数）时，证明了不等式：Ｒｅ［ｔｒ（ＡＢ）￣ｎ］≤Ｒｅ［ｔｒＡ￣ｎＢ￣ｎ］成立，其中Ａ，Ｂ为半正定四元数四共轭矩阵。

It is proved that when n=2￣t (t is natural number)inequality Re [tr (AB)￣n]≤Re[tr A￣nB￣n]is true,where A,B are semi-definite self-conjugate quaternion matrices.Re(trM)is real part of trM.