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