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线性代数应该这样学

第四版

作者：Sheldon Axler（谢尔顿·阿克斯勒）
译者：吴俊达、何阳

很高兴，能和大家分享由我们翻译的《线性代数应该这样学》（Linear Algebra Done Right）第四版的中文版。该译本（与原书一样）采用 知识共享署名-非商业性使用 4.0 国际许可协议(CC BY-NC 4.0) 进行许可。其电子版下载链接如下：（如果访问其中一个链接不成功，可尝试访问其他链接）

该译本无纸质版。如有需要，可自行打印。但请注意，如版权许可中的 NC（NonCommercial，非商业性使用）所要求，打印版与电子版均不得用于出售。

关于本书

关于原书的介绍详见作者主页的介绍。本书的主要特色及讨论的主题摘录如下：

本书采用的新颖思路将行列式搁置于全书末尾，将重点放在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。作者在指明定义概念的动机以及简化证明方面下了一番功夫。每章附有大量有趣的习题，这些习题有助于学生理解与熟练运用线性代数的知识。

本书除要求读者具有适当数学素养之外，不对预备知识做出要求。本书首先讨论向量空间、线性无关性、张成空间、基和维数，然后讨论线性映射、特征值和特征向量。接着，本书介绍内积空间，由此引出有限维向量空间中的谱定理及其若干推论（如奇异值分解）。此后，本书利用广义特征向量来在线性算子的结构方面给读者以启发。最后，借助交错多重线性型，以简洁的方式引入了行列式。
新版本相较于上一版的改动，节选整理如下：
《线性代数应该这样学》（Linear Algebra Done Right）第四版新增了二百五十余道习题和七十余个例子，全书还讨论了数个新的主题且有多处改进。「第四版中的主要改进和补充」见原书 PDF 文件的第 xvi 页（对应于译本的第 xi 页）。
希望我们的翻译能帮助大家跨越“语言关”，更深入地掌握书中关于向量空间和线性映射的基本内容。

欢迎读者朋友们多提意见和建议，可将其发送至 ladr2024@163.com。

勘误表见 此处。

相关链接

Linear Algebra Done Right

fourth edition

Author：Sheldon Axler
Translators：吴俊达(Oliver Wu)、何阳(He Yang)

We are happy to share with you our Chinese translation of the fourth edition of Linear Algebra Done Right as an Open Access book. The electronic version of this translation with a Creative Commons BY-NC license is available without cost at the links below. (If one of the links doesn't work, just try the others.)

There is no print version of the translation. You can print it yourself if necessary, but you cannot sell either the printed version or the electronic version, as specified by the NC (NonCommercial) part of the copyright license.

About the Book

For more information about the English version, see the author's page. According to that page, the main features and topics of this book are as follows:

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.

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 then introduced, leading to the finite-dimensional spectral theorem and its consequences such as the singular value decomposition. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. Determinants are cleanly introduced via alternating multilinear forms.
The major improvements and additions (compared to the previous edition) are:
The fourth edition of Linear Algebra Done Right contains over 250 new exercises and over 70 new examples, along with several new topics and multiple improvements throughout the book. See page xvi in the PDF file for the English version (corresponding to page xi in the PDF file for the Chinese version) for a list of major improvements and additions in the fourth edition.
It's hoped that our translation will help you to overcome the "language barrier" and attain a deep understanding of vector spaces and linear maps.

Comments or suggestions about the translation of the fourth edition of Linear Algebra Done Right can be sent to the translators at ladr2024@163.com.

Click here for the errata.

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