摘要：幂等矩阵在数学领域以及其他许多领域应用都非常广泛，因此对幂等矩阵进行探讨具有很重要的意义。本文归纳总结了幂等矩阵的一些性质和结论，研究了幂等矩阵的运算和幂等矩阵线性组合的幂等性并根据幂等矩阵的性质解决部分相关问题，即给出幂等矩阵的部分相关应用.

关键词:幂等矩阵; 性质; 应用

Abstract: The idempotent matrix is widely applied in mathematics and many other fields, so there is a very vital significance to carry on the discussion to the idempotent matrix. The main purpose of this paper is to summarize some simple nature and some important conclusions of idempotent matrix. First, this paper carries on the induction summary to its simple nature. Then it discusses the operation of idempotents and the idempotency of  linear combinations of two idempotent matrices, how to solve the part of the associative questions based on the properties of the idempotent matrix, and this is the part of applications of the idempotent matrix.

Key words: the idempotent; the properties;  the application