| 线性变换的值域与核的维数关系定理的证法探析 |
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| 引用本文： | 刘妮.线性变换的值域与核的维数关系定理的证法探析[J].数学学习,2022,25(1):13-14,36. |
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| 作者姓名： | 刘妮 |
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| 作者单位： | 陕西师范大学数学与统计学院,陕西西安710119 |
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| 基金项目： | 陕西师范大学教师教学模式创新与实践研究专项基金项目 |
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| 摘 要： | 本文首先证明了有限维线性空间上的线性变换是单射当且仅当它是满射这一结论,其次分析了通常高等代数教材中关于线性变换的值域与核的维数关系定理的两种证明方法,并给出了该定理的一种新的证明方法.
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| 关 键 词： | 线性空间 线性变换 值域 核 维数 |
On Proofs of the Relation between Dimensions of Image and Kernel of a Linear Transformation |
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| LIU Ni.On Proofs of the Relation between Dimensions of Image and Kernel of a Linear Transformation[J].Studies In College Mathematics,2022,25(1):13-14,36. |
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| Authors: | LIU Ni |
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| Affiliation: | (School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China) |
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| Abstract: | The result that a linear transformation on a finite dimensional linear space is injective if and only if it is surjective is proved directly.Two common proofs for the relation between dimensions of a linear transformation's image and kernel are analyzed and a new proof for this relation is given. |
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| Keywords: | linear spaces linear transformation image kernel dimension |
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