自共轭四元数矩阵的几个不等式

Several inequalities of self-conjugate quaternion matrices

主要讨论了自共轭四元数矩阵的不等式问题,得到了四元数向量和四元数正定矩阵的Schwartz型不等式,在此基础之上,给出了两个Rayleigh商乘积的上下界。

The inequalities of self-conjugate quaternion matrix were discussed.The Schwartz type inequalities for quaternion positive definite matrix and the vector of quaternion were presented.Basing on the inequality above,The upper bound and lower bound for the product of two Rayleigh divisions were obtained.