幂等矩阵的性质及其推广

Properties and Generalization of Idempotent Matrix

首先对幂等矩阵的简单性质进行了归纳总结,接着论证了幂等矩阵的等价条件及其特征值的取值范围,并讨论了幂等矩阵与实对称矩阵的关系、幂等矩阵与其伴随矩阵的特征值和特征向量的对应关系及幂等矩阵在群逆中的一个性质.最后讨论了幂等矩阵的两种分解形式.

Firstly,the simple properties of idempotent matrices are summarized,then the equivalence conditions of idempotent matrices and the range of their eigenvalues are proved,and the relations between idempotent matrices and real symmetric matrices,the corresponding relations between idempotent matrices and eigenvectors of their adjoint matrices,and the properties of idempotent matrices in group inverses are discussed.Finally,two decomposition forms of idempotent matrices are discussed.