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环中个倍幂等换子与个倍对换子可逆性问题。

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

摘要证明了数个同阶幂等阵相似充要条件是它们有相同秩；给出了幂等阵相似标准型；讨论了个幂等阵线性组仍是幂等阵充要条件。