中文摘要：

利用线性代数的方法，证明每个方阵都能分解为一个幂等阵与一个可逆阵的和且二者可交换，也可以表示为一个幂等阵与一个可逆阵的乘积．

英文摘要：

By means of the methods of linear algebras, proved that every square matrix can be expressed as the sum of an idempotent matrix and an invertible matrix which commute with each other, and also can be written as the product of an idempotent matrix and an invertible matrix.