中文摘要：

以矩阵方幂的秩为基本工具,对秩与非零特征值个数的差为1或2的矩阵做了等价刻画。作为应用,只用矩阵的秩可给出相应矩阵的Jordan标准形。

英文摘要：

With the rank of matrix square power as a basic tool,some equivalent characterization of matrices was presented,in which the differences between the rank and number of non-zero eigenvalues is equal to 1 or 2. As applications,Jordan canonical form of the matrices can be given simply by the rank of the matrices.