线性代数 II

学习材料

教科书

中文

1. [1]
   蓝以中, 高等代数简明教程, 3rd ed., vol. 2, 2 vols. in 北京大学数学教学系列丛书. 北京: 北京大学出版社, 2023. Accessed: May 05, 2026. [Online]. Available: https://book.douban.com/subject/36553626/
2. [2]
   丘维声, 简明线性代数, 2nd ed. in 普通高等教育十一五国家级规划教材. 北京: 北京大学出版社, 2024. Accessed: May 06, 2026. [Online]. Available: https://book.douban.com/subject/37101517/
3. [3]
   丘维声, 高等代数, 1st ed., vol. 2, 2 vols. 北京: 清华大学出版社, 2010. Accessed: May 05, 2026. [Online]. Available: https://www.tup.com.cn/booksCenter/book_03258702.html
   其它链接：

   • https://www.wqbook.com/books/booksn/032587-02

   免费资源：

   样章

   • https://www.tup.com.cn/upload/books/yz/032587-02.pdf

4. [4]
   丘维声, 高等代数, 2nd ed., vol. 2, 2 vols. 北京: 清华大学出版社, 2019. Accessed: May 05, 2026. [Online]. Available: https://www.tup.com.cn/booksCenter/book_07292503.html
   其它链接：

   • https://www.wqbook.com/books/booksn/072925-03
5. [5]
   丘维声, 高等代数学习指导书, 2nd ed., vol. 2, 2 vols. 北京: 清华大学出版社, 2016. Accessed: May 05, 2026. [Online]. Available: https://www.tup.com.cn/booksCenter/book_05702804.html
   其它链接：

   • https://www.wqbook.com/books/booksn/057028-04

   免费资源：

   • https://www.tup.com.cn/upload/books/yz/057028-04.pdf
6. [6]
   谢启鸿, 姚慕生, and 吴泉水, 高等代数学, 4th ed. in 普通高等教育“十二五”国家级规划教材. 复旦大学出版社, 2022. Accessed: May 11, 2026. [Online]. Available: https://www.fudanpress.com/505429541603282944/detail/book?bookId=387892&bookIdentifier=352220686345d7&company_id=569&company_identifier=2959846655452a&navGuid=505756482248159232
7. [7]
   谢启鸿 and 姚慕生, 高等代数, 4th ed. 复旦大学出版社, 2022. Accessed: May 11, 2026. [Online]. Available: https://www.fudanpress.com/505429541603282944/detail/book?bookId=387893&bookIdentifier=550759686345d8&company_id=569&company_identifier=2959846655452a&navGuid=505756482248159232
8. [8]
   姚慕生, 吴泉水, and 谢启鸿, 高等代数学, 3rd ed. in 普通高等教育“十二五”国家级规划教材. 复旦大学出版社, 2014. Accessed: May 11, 2026. [Online]. Available: https://www.fudanpress.com/505429541603282944/detail/book?bookId=382947&bookIdentifier=7829146863320f&company_id=569&company_identifier=2959846655452a&navGuid=505756482248159232
9. [9]
   姚慕生 and 谢启鸿, 高等代数, 3rd ed. 复旦大学出版社, 2015. Accessed: May 11, 2026. [Online]. Available: https://www.fudanpress.com/505429541603282944/detail/book?bookId=383616&bookIdentifier=7410686863349d&company_id=569&company_identifier=2959846655452a&navGuid=505756482248159232

英文

10. [10]
    S. Axler, Linear Algebra Done Right, 4th ed. Springer, 2026. Accessed: Sep. 10, 2026. [Online]. Available: https://linear.axler.net/index.html
    免费资源：

    • PDF (CC-BY-NC-4.0)
11. [11]
    C. D. Meyer, Matrix Analysis and Applied Linear Algebra, 2nd ed. in Other Titles in Applied Mathematics, no. OT188. Society for Industrial and Applied Mathematics, 2023. doi: 10.1137/1.9781611977448.
12. [12]
    R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed. Cambridge University Press, 2013. doi: 10.1017/CBO9781139020411.
    其它链接：

    • Cambridge Aspire
13. [13]
    S. R. Garcia and R. A. Horn, Matrix Mathematics, 2nd ed. in Cambridge Mathematical Textbooks. Cambridge: Cambridge University Press, 2023. doi: 10.1017/9781108938426.
14. [14]
    L. N. Trefethen and D. Bau III, Numerical Linear Algebra, 25th Anniversary. in Other Titles in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2022. doi: 10.1137/1.9781611977165.

指导书

中文

15. [15]
    任广千, 谢聪, and 胡翠芳, 线性代数的几何意义. 西安: 西安电子科技大学出版社, 2015. Accessed: May 06, 2026. [Online]. Available: https://www.xduph.com/Pages/BookDetail.aspx?doi=13bc748f-fbb6-426a-9a59-1cab34fa991e

英文

16. [16]
    C. D. Meyer, Matrix Analysis and Applied Linear Algebra: Study and Solutions Guide, 2nd ed. in Other Titles in Applied Mathematics, no. OT189. Society for Industrial and Applied Mathematics, 2023. doi: 10.1137/1.9781611977462.

公开课

中文

17. [17]
    清华大学. 北大丘维声教授清华高等代数课程1080P高清修复版(全151集). Accessed: May 05, 2026. [Online Video]. Available: https://www.bilibili.com/video/BV1jR4y1M78W

    主讲：丘维声

    建议倍速：1.25×–1.5×

18. [18]
    谢启鸿, 复旦大学. 【数学专业课】高等代数学-复旦大学-谢启鸿-高清, (Dec. 14, 2019). Accessed: May 11, 2026. [Online Video]. Available: https://www.bilibili.com/video/BV1mJ411r7ZB/

    主讲：谢启鸿

参考资料

教科书

中文

19. [19]
    李炯生, 查建国, and 王新茂, 线性代数, 2nd ed. in 中国科学技术大学精品教材. 安徽 合肥: 中国科学技术大学出版社, 2010. Accessed: May 06, 2026. [Online]. Available: https://book.douban.com/subject/4200433/
20. [20]
    席南华, 基础代数, vol. 2, 3 vols. 北京: 科学出版社, 2018. Accessed: May 06, 2026. [Online]. Available: https://www.ecsponline.com/goods.php?id=189397
21. [21]
    李尚志, 线性代数（数学专业用）. in “十五”国家规划教材. 北京: 高等教育出版社, 2006. Accessed: May 06, 2026. [Online]. Available: https://www.hep.com.cn/book/show/9b998ecf-0298-4031-8d38-fa5e9187cbb3
22. [22]
    张贤科 and 许甫华, 高等代数学, 2nd ed. 北京: 清华大学出版社, 2004. Accessed: May 11, 2026. [Online]. Available: https://www.tup.com.cn/booksCenter/book_00937505.html
    其它链接：

    • 豆瓣读书
23. [23]
    张贤科, 高等线性代数. 北京: 高等教育出版社, 2012. Accessed: May 11, 2026. [Online]. Available: https://www.hep.com.cn/book/show/327efefa-8d7a-44af-83a1-a08c18e1421d
    其它链接：

    • 豆瓣读书
24. [24]
    Костри́кин А. И., 代数学引论, 牛凤文, Trans., 3rd ed., vol. 2, 3 vols. in 俄罗斯数学教材选译. 北京: 高等教育出版社, 2007. Accessed: May 06, 2026. [Online]. Available: https://www.hep.com.cn/book/show/c8de259a-06c4-4b29-ac8c-1cbb7a677b11

英文

25. [25]
    S. Lang, Linear Algebra, 3rd ed. in Undergraduate Texts in Mathematics. New York, NY: Springer, 2013. doi: 10.1007/978-1-4757-1949-9.
26. [26]
    M. Artin, Algebra, 2nd ed. Pearson, 2014. Accessed: May 06, 2026. [Ebook]. Available: https://www.amazon.com/Algebra-Michael-Artin-ebook/dp/B00HR7MSZO
27. [27]
    P. D. Lax, Linear Algebra and Its Applications, 2nd ed. in Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley-Interscience, 2013. Accessed: May 05, 2026. [Online]. Available: https://www.wiley.com/en-us/Linear+Algebra+and+Its+Applications%2C+2nd+Edition-p-9781118626924

指导书

中文

28. [28]
    李尚志, 线性代数学习指导. in 高校核心课程学习指导丛书. 合肥: 中国科学技术大学出版社, 2015. Accessed: May 06, 2026. [Online]. Available: https://book.douban.com/subject/26390093

视频

29. [29]
    分析学爱好者, 我为什么推荐你使用丘维声学习高等代数, (Sep. 23, 2025). Accessed: May 05, 2026. [Online Video]. Available: https://www.bilibili.com/video/BV1kkJyzcE4q

习题集

中文

30. [30]
    Костри́кин А. И., 代数学习题集, 丘维声, Trans., 4th ed. in 俄罗斯数学教材选译. 北京: 高等教育出版社, 2018. Accessed: May 06, 2026. [Online]. Available: https://www.hep.com.cn/book/show/df4ba4fe-893d-4400-888e-311125e975a4

其它

英文

31. [31]
    J. Lu, “Matrix Decomposition and Applications,” Aug. 01, 2025. doi: 10.48550/arXiv.2201.00145.
    免费资源：

    • PDF (arXiv)