幂等矩阵的充要条件及证明

The evidence of the necessary and sufficient conditions for Idempotent matrix

满足2A=A的n阶方阵A称为幂等矩阵,它是矩阵环nM(K)的一个幂等元,它与空间的分解、不变子空间的研究有密切关系。利用线性空间的理论方法研究幂等矩阵的性质,证明了与它等价的一些充要条件。

A matrix of satisfying A= A^2 is called idempotent matrix. It is an idempotent element of matrix ring Mn （F）. It is closely related to decomposition of space and invariant subspace.Some properties of idempotent matrix is discussed by using methods of linear space. The necessary and sufficient conditions for idempotent matrix is given.