This paper is a study on the invertibility of the commutator of scalar-idempotent elements and scalar-involutory elements of a unitary ring.

本文研究在一个有单位的环中两个倍的换位子与两个倍对的换位子的可逆性。

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

要证明了数域上两个同阶阵相似的充要条件是它们有相同的秩；给出了阵的相似标准型；讨论了两个阵的线性组仍是阵的充要条件。