关于幂等矩阵一个充要条件的证明

The proof of a sufficient and necessary condition on idempotent matrices

幂等矩阵及其等价条件在矩阵理论和模糊数学中都有重要应用.在已有结论基础上,将幂等矩阵的一个必要条件完善成了充要条件,并运用矩阵的降秩定理给出该问题一个新的充分性的证明方法,是对已有证明方法的补充和完善。

Idempotent matricesand its equivalent conditions play important roles in matrix theory and fuzzy mathematics. A necessary condition of idempotent matrices could be shifted to the sufficient and necessary condition,and reduced- rank theorem of matrices is applied to testify this problem sufficiently for the first time,which is a supplement and improvement to the original proof methods.