| 浅议线性代数教学中的几何直观 |
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| 引用本文： | 赵素云.浅议线性代数教学中的几何直观[J].科技咨询导报,2013(16):154-155,157. |
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| 作者姓名： | 赵素云 |
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| 作者单位： | 中国人民大学数据工程与知识工程教育部重点实验室 北京100872 |
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| 基金项目： | 中国人民大学研究基金（中央高校基本科研业务费专项资金资助）项目成果（12XNLF07）; 国家自然科学基金（61202114）资助 |
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| 摘 要： | 该文讨论了几何直观在线性代数教学中的重要性,对几个较为抽象的代数观念如:线性相关、线性无关、行列式、直和等以及一些常用代数方法如:斯密特正交化、最小二乘法等总结出了它们在二维或三维欧氏几何中的相应解释,结合几个例子说明了代数与几何之间的紧密联系,说明了在线性代数教学中贯彻数形结合思想的重要性.
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| 关 键 词： | 线性代数 几何直观 数形结合 教学方法 解析几何 |
Key Laboratory of Data Engineering and Knowledge Engineering |
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| ZHAO Suyun.Key Laboratory of Data Engineering and Knowledge Engineering[J].Science and Technology Consulting Herald,2013(16):154-155,157. |
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| Authors: | ZHAO Suyun |
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| Institution: | ZHAO Suyun (Renmin University of China,MOE,Beijing,China,100872) |
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| Abstract: | this paper discusses about the importance of geometric intuition in linear algebra.First,we provide the 2--dimension/3--dimension euclidean geometric meaning of several abstract algebraic concepts, such as linearly dependence,linearly independence, determinant and direct sum.Further,we provide the 2--dimension/3--dimension euclidean geometric meaning of some common algebraic methods, Such as schmidt orthogonalization and least square method.By some illustrative examples,we finally show the relationship between algebra and geometry and point out the importance of symbolic--graphic combination in education of linear algebra. |
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| Keywords: | linear algebra geometric intuition symbolic-graphic combination teaching method analytic geometry |
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