The necessary and sufficient conditions of similarity of two idempotent matrices are proved, the idempotency of linear combinations of two idempotent matrices is discussed.

• 摘要证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩；给出了幂等阵的相似标准型；讨论了两个幂等阵的线性组合仍是幂等阵的充要条件。