Criterions of partial stable matrix and normal form of partial positive de? nete matrix are given, some conditions of solvability and uniqueness of Lyapunov matrix equation are discussed. Furthermore, some prob-lems for further study are presented. 给出了部分稳定矩阵的几种判据与部分位正定矩阵的标准型,研究了矩阵方程可解性、唯一性的几种条件,提出一些可供进一步研究的问题。