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[交流] 【原版教材•中英对照】线性代数应该这样学已有1人参与

Linear Algebra Done Right
线性代数应该这样学

Author: Sheldon Axler

下载地址：https://www.zhisci.com/pdfshow/17753

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
这本最畅销的线性代数第二课程教材是针对本科生数学专业和研究生。这里采用的新颖方法将决定因素排除在本书末尾。本文着重于线性代数的中心目标：理解有限维向量空间上线性算子的结构。作者特别注意激发概念和简化证明。每章都有各种有趣的练习，帮助学生理解和操作线性代数的对象。

The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
第三版包含了整本书的主要改进和修订。自上一版本以来，增加了300多个新的练习。增加了许多新的例子来说明线性代数的关键思想。书中涉及的新主题包括乘积空间、商空间和对偶空间。漂亮的新格式创建的页面在打印版和电子版中都有异常令人愉快的外观。

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
除了对适当数学成熟度的通常要求外，没有任何先决条件被假定。因此，本文首先讨论向量空间、线性独立性、跨度、基和维数。这本书然后处理线性映射，特征值，和特征向量。引入内积空间，得到有限维谱定理及其结果。然后使用广义特征向量来深入了解线性算子的结构。

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