中文摘要：

对秩与非零特征值个数的差为3的矩阵给出了应用矩阵指数、矩阵秩为基本工具的充要条件,作为应用得到了这样矩阵的Jordan标准形和Drazin逆的表达形式。

英文摘要：

By using matrix index and rank of matrices as basic tools, this paper gave out some necessary and sufficient conditions for the difference between rank and number of non-zero eigenvalues of matrices being 3. As applications, it obtained the expression for Jordan canonical form and Drazin inverse of this kind of matrices.