摘要
给出并证明了齐次和非齐次线性方程组等价的充要条件,由此得到了保秩矩阵乘积的一系列结果.应用该充要条件研究了矩阵方幂秩的规律以及伴随矩阵的性质,并由此给出了两个有关幂等阵和幂零阵的伴随矩阵定理的简捷证明。
Necessary and sufficient conditions of equivalent linear systems are given and proved, and a series results of rank-preserving matrix multiplication are obtained. Rank of power matrix and adjiont matrix are investigated by using obtained NS conditions. Finally, a simple proof of two theorems about adjiont matrice of idempotent and nilpotent matrice is given.
基金
湖南省自然科学基金(03JJY3014)
湖南省教育厅科研项目(02C355)资助
关键词
线性方程组等价
充要条件
保秩乘积
幂等阵
幂零阵
伴随矩阵
equivalent linear system, necessary and sufficient condition, rank-preserving matrix muldplication, idempotent matrix, nilpotent matrix, adjiont matrix
