| 线性方程组等价的充要条件及其应用 |
| |
| 引用本文： | 唐建国. 线性方程组等价的充要条件及其应用[J]. 零陵学院学报, 2004, 0(5) |
| |
| 作者姓名： | 唐建国 |
| |
| 作者单位： | 零陵学院数学与计算科学系 湖南 |
| |
| 基金项目： | 湖南省自然科学基金(03JJY3014)，湖南省教育厅科研项目(02C355)资助 |
| |
| 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。
|
| 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 |
Necessary and Sufficient Conditions of Equivalent Linear Systems and Its Applications |
| |
| TANG Jian-guo. Necessary and Sufficient Conditions of Equivalent Linear Systems and Its Applications[J]. Journal of Hunan University of Science and Engineering, 2004, 0(5) |
| |
| Authors: | TANG Jian-guo |
| |
| Abstract: | 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. |
| |
| Keywords: | equivalent linear system necessary and sufficient condition rank-preserving matrix muldplication idempotent matrix nilpotent matrix adjiont matrix |
| 本文献已被 CNKI 等数据库收录！ |
