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

本文研究在一有元的环中倍幂等元的换子与倍对元的换子的可逆性问题。

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

摘要证明了数域上阶幂等阵相似的充要条件是它们有相的秩；给出了幂等阵的相似标准型；讨论了幂等阵的线性组仍是幂等阵的充要条件。