摘要
利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.
In this paper, some equivalent conditions for m(m ≥ 2) times idempotent matrices are given by using rank of matrices and dimensions of solution spaces of homogeneous linear systems. Consequently, the results as m = 2 and m = 3 are generalized. Also, the corresponding results are generalized to rn times idempotent linear transformations.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第23期190-193,共4页
Mathematics in Practice and Theory
基金
广东省自然科学基金(8151601501000002
9151051501000066)
广东惠州学院项目(C_210.0216
C_211.0106
JG2010008)
关键词
m次幂等矩阵
矩阵的秩
齐次线性方程组
解空间的维数
m次幂等线性变换
m times idempotent matrices
rank of matrices
homogeneous linear systems
dimensions of solution spaces
m times idempotent linear transformations