每个矩阵都能表成两个秩幂等矩阵之和

Everymatrix is a sum of two rank-idempotent matrices

研究了秩幂等矩阵的性质及两个秩幂等矩阵的线性组合的结构,利用矩阵的广义逆,矩阵的若当标准形与矩阵的有理标准形,得出了秩幂等矩阵的一些新的特征,并证明了每个矩阵都能表成两个秩幂等矩阵之和。

This paper researches some properties of rank-idempotent matrix,and the linear combinations structures of two rank-idempotent matrices.By using the generalized inverse of matrix,the Jordan canonical form of matrix and the rational canonical form of matrix,we get some new characters of rank-idempotent matrix,and prove that every matrix is a sum of two rank-idempotent matrices.