| 矩阵秩概念开发上的一个更简洁更干净的处理 |
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| 引用本文： | 郭聿琦,;王正攀,;梁星亮.矩阵秩概念开发上的一个更简洁更干净的处理[J].高等理科教育,2014(4):89-91. |
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| 作者姓名： | 郭聿琦 ;王正攀 ;梁星亮 |
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| 作者单位： | [1]兰州大学数学与统计学院,甘肃兰州730000; [2]西南大学数学与统计学院,重庆400715 |
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| 基金项目： | 国家自然科学某余资助项目（项目编号：11371177）. |
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| 摘 要： | 矩阵秩概念的通常开发,无论是"几何"的,还是代数的,其关键步骤不易理解,这里指的不是理论上的理解,而是指获取"矩阵的行秩等于其列秩"的直观感。文章相对于"元向量组在涉及向量的初等变换下其秩不变"的事实,平行地建立了"元向量组在涉及分量的初等变换下其秩不变"的事实,从而给出了矩阵秩概念开发上的关键步骤(行秩等于列秩)的一个简洁的处理。
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| 关 键 词： | 矩阵 矩阵的秩 矩阵初等变换 |
A Briefer and Cleaner Treatment on the Concept Development of Matrix Rank |
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| Institution: | GUO Yu - qi , WANG Zheng -pan, LIANG Xing - liang ( 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China; 2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China) |
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| Abstract: | For the usual development of the concept of matrix rank, the key steps are not easy to understand whether in ＂ Geometry＂ or in algebra, here refers to be not understanding on theory, but to obtain the intuitive sense for the fact that ＂ Row Rank of a Matrix is Equal to the Column Rank＂ . In the paper, relative to the fact that ＂ the Rank of a System of Vectors of N - tuples is Invariant under Elementary Transformations for Vectors＂ , we establish the fact that ＂ the Rank of a System of Vectors of N - tuples is Invariant under El- ementary Transformations for Components＂ in parallel, and then present a briefer treatment on the key step （ the row rank of a matrix is equal to the column rank ） on the development of matrix rank. |
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| Keywords: | matrix rank of matrices elementary transformations of matrices |
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