分块矩阵的正定性准则及其应用(英文)  

A Criterion for the Positive Definiteness of A Block-Matrix and Its Application

作　　者：刘向华 

机构地区：[1]株洲师专数学系,株洲市412007

出　　处：《数学理论与应用》2001年第3期122-128,共7页Mathematical Theory and Applications

摘　　要：本文给出了 3× 3分块矩阵的一个正定性判定准则 ,应用这个准则 ,给出了矩阵方程 (ATXB ,BT×B)=(C ,D)A criterion for the positive definiteness of symmertic 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.

关 键 词：分块矩阵 正定性 判定准则 矩阵方程 正定解 充分条件 通式 

分 类 号：O151.21[理学—数学]