矩阵的复正定性与A■=b的反问题求解

COMPLEX POSITIVEDEFINITE MATRIX AND SOLUTION OF INVERSE QUESTION FOR "A■=B"

本文主要讨论线性方程组A■=b的反问题.得到了A■=b在复正定矩阵类中有解的充要条件,给出了A■=b在复正定类中解的一般形式.并同时得到用低阶矩阵来判定高阶矩阵复正定性的方法,推广了郭忠文中的定理1。

This paper discusscd inverse problem on system of equation'A■=b',a necessary and sufficient condition on existence of solutionfor A■=b in complex poxsitivedefinite matrix is given,a general formof solution for A■=b in complex positivedefinite matrix is obtained onthe other hand,we report a method in which complex positivedefinite ofmatrix is judged by low-order matrix,theorem lin refence[1]has beengeneralized.