关于正定四元数方阵的注记

A NOTE ON THE POSITIVE DEFINITE QUATERNION MATRIX

这篇文章给出了四元数方阵为正定的充要条件，另外还给出了线性方程组 Ａｘ ＝ β的反问题具有正定四元数方阵解的充要条件，以及线性方程组Ａｘ ＝

In this paper a necessary and sufficient condition is given for the quaternion matrix to be positive definite.In addition a necessary and sufficient condition is fund for the inuerse problem of the system of Li near equations Ax=β to have a solution of positive definite quaternion matrix as well as the general form of solutions of positive definite quater nion matrices is given for the inverse problem of the system of Li near equations Ax=β . In this paper a necessary and sufficient condition is given for the quaternion matrix to be positive definite.In addition a necessary and sufficient condition is fund for the inuerse problem of the system of Li near equations Ax=β to have a solution of positive definite quaternion matrix as well as the general form of solutions of positive definite quater nion matrices is given for the inverse problem of the system of Li near equations Ax=β .