Introduction to Linear Algebra

Gilbert Strang

出版时间

2016-08-31

ISBN

9780980232776

评分

★★★★★
AI导读
核心看点
  • MIT经典教材,以几何直觉重塑线代认知
  • 新增SVD与概率统计章节,强化数据应用
  • 四大子空间视角,打通理论与计算壁垒
适合谁读
  • 计算机、工程及经济类数学基础学习者
  • 机器学习与数据科学领域的进阶研究者
  • 渴望摆脱枯燥定义、追求深层理解的读者
读前提醒
  • 建议配合MIT 18.06视频课程同步学习
  • 英文原版阅读有门槛,可参考中文译本
  • 需主动梳理知识点,书风似讲义较跳跃
读者共识
  • 公认线代教材巅峰,深入浅出体验极佳
  • 相比国内教材,更重直观理解而非计算
  • 虽无中文原版,但口碑极高值得硬啃

本导读基于书籍简介、目录、原文摘录、短评和书评生成,不等同于全文精读。

精彩摘录
  • "we needed to open linear algebra to the world"
  • "Let me connect these special matrices A and S to calculus. The vector x changes to a function x(t). The differences Ax become the derivative dx/ dt = bet). In the inverse direction, the sum Sb becomes the integral of bet)."
  • "When E multiplies on the right, it acts on the columns of A."
  • "Schur complement."
  • "To solve A x = b without A-I, we deal with one column b to find one column x."
  • "Suppose there is a nonzero vector x such that Ax = 0"
  • "A triangular matrix is invertible if and only if no diagonal entries are zero."
  • "The column space C (U) consists of all vectors of the form (b I , b2 , b3 , 0)."
作者简介
Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT, an Honorary Fellow of Balliol College, and a member of the National Academy of Sciences. Professor Strang has published eleven books: Differential Equations and Linear Algebra (2014) Introduction to Linear Algebra (1993,1998,2003,2009) Linear Algebra and Its Applications (1976,1980,1988,2005) An Analysis of the Finite Element Method, with George Fix (1973, 2008) Introduction to Applied Mathematics (1986) Calculus (1991) Wavelets and Filter Banks, with Truong Nguyen (1996) Linear Algebra, Geodesy, and GPS, with Kai Borre (1997) Computational Science and Engineering (2007) Essays in Linear Algebra (2012) Algorithms for Global Positioning, with Kai Borre (2012) He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. His home page is math.mit.edu/~gs/ and his video lectures on linear algebra and on computational science and engineering are on ocw.mit.edu (mathematics/18.06 and 18.085).
目录
1 Introduction to Vectors
2 Solving Linear Equations
3 Vector Spaces and Subspaces
4 Orthogonality
5 Determinants

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用户评论
其实更喜欢 Strang教授的 Lectures,Textbook太想做到循循善诱了,反而降低了阅读流畅度。
线性代数教材巅峰之作。你会知道什么叫深入浅出,原来数学课本可以读来如此舒适。
一刷,建立了linear algebra的big picture,以及初步有了一个whole view。
本科的时候可能学了个假线代。配合MIT的18.06视频效果拔群。
开始还不以为然,看到第三章null space 开始觉得非常精彩。第一本更强调几何直觉,如果带着这些几何图像去研读这一本,定会收获更清晰的直觉。P311 第23题
有电子版和答案,需要加v a765426599
"utterly beautiful" --鸽兰特
我学完的第一本英文教材书,教材编的真的棒,小结,例子,配图都非常用心,不仅仅从数学的角度介绍线代,很多精力放在了实际应用的例子上,不会像本科期间的教材,学的不知所以然,仅变成了分数的奴隶。
去年年初看的了,老爷子很可爱。也算是为其他目的读的第一本英文书
想起来高中时教线代的老师,其使用的教学方法比起这本书来并无差距(也不排除是借鉴)。只想说高中老师太牛了
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