摘要
研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.
Necessary and sufficient（NS） conditions for unit-ponent matrices are explored. A NS condition for unit-ponent matrices as m=2 is generalied to general unit-ponent matrices by using rank of matrices and dimension of solution spaces of homogeneous linear systems,and a result that unit-ponent matrices are diagonalizable is obtained.Finally, the NS conditions for unit-ponent matrices are parallelly generalied to unit-ponent linear transformations.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第20期172-176,共5页
Mathematics in Practice and Theory
基金
惠州学院科研项目
关键词
幂幺矩阵
充要条件
矩阵的秩
解空间的维数
unit-potent matrix
necessary and sufficient condition
rank of matrix
dimension of solution space
