摘要
设Ａ是一个ｎ阶实四元数方阵，若对任意的非零ｎ元列向量ｘ，有ｘ＊Ａｘ的实部非负，则称Ａ是一个实部半正定阵．本文给出了实四元数矩阵方程组ＸｎｎＡｎｓ＝ＡｎｓＸｎｎＢｎｔ＝Ｏｎｔ｛有实部半正定解的充要条件及其解集的表达式．
n n×n real quaternion matrix A is termed Re psd if the real part of x *Ax≥0 for every nonzero quaternion n vector x. In this paper a necessary and sufficient condition for the existence of and the expression for Re psd solution of the system of quaternion matrix equations X nn A ns =A ns X nn B nt =O nt are derived.
出处
《纯粹数学与应用数学》
CSCD
1998年第2期43-46,共4页
Pure and Applied Mathematics
基金
山东省自然科学基金
关键词
四元数体
矩阵方程组
实部半正定阵
the quaternion field
matrix equation system
Re psd matrix
