摘要
设Ｆ是一个具有对合反自同构的体，Ω是一个实四元数体．本文在Ｆ上定义了次自共轭矩阵，在Ω上定义了（半）正定次自共轭矩阵及亚（半）正定次自共轭阵，给出了Ω上分块矩阵为亚（半）正定次自共轭阵的充要条件；
Let F, Ω be a skew field with an involutorial antiautomorphism, the real quaternion field respectively. In this paper we define a minor self_conjugate matrix over F , a positive (semi)definite minor self_conjugate and a metapositive (semi)definite minor self_conjugate matrix over Ω ,and give a necessary and sufficient condition for that a partitioned matrix is metapositive (semi)definite minor self_conjugate. Moreover, for a linear matrix equation AX=B , we get necessary and sufficient conditions of its existence and its expressions of minor self_conjugate matrix solutions and metapositive (semi)definite minor self_conjugate solutions of the matrix equation.
出处
《曲阜师范大学学报（自然科学版）》
CAS
1997年第1期32-37,共6页
Journal of Qufu Normal University(Natural Science)
基金
山东省自然科学基金
关键词
矩阵方程
分块矩阵
自共轭矩阵
半正定
亚正定
skew field metapositive (semi)definite minor self_conjugate matrix matrix equation
