摘要
给出了一个3×3分块矩阵的正定性判别准则,应用该准则,导出了矩阵方程(AT XA,B TXB)=(C,D)有正定解的充要条件及一般表达式.
A criterion for the positive definiteness of symmetric 3 × 3 block-matrix A is presented. Applying the criterion, we derive the necessary and sufficient conditions for that the matrix equation （A^TXA, B^TXB） = （C,D） has positive definite solution. The expression of the general solution is given.
出处
《湖南文理学院学报（自然科学版）》
CAS
2006年第4期16-20,共5页
Journal of Hunan University of Arts and Science(Science and Technology)
关键词
正定阵
矩阵方程
分块矩阵
奇异值分解
positive definite matrix
matrix equation
block matrix
singular decomposition
