有限维向量空间

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• ten_fingers · 2012 年

  ……矩阵求逆、线性规划（优化）的单纯形算法以及网络线性规划。本·诺布尔（Ben Noble）写的线性代数是一本很好的入门教材。而皇冠上的明珠则是保罗·哈尔莫斯（Paul Halmos）的《有限维向量空间》（Finite Dimensional Vector Spaces），这是哈尔莫斯给冯·诺依曼当助手时写的；该书处理线性代数的方式非常像泛函分析，因此可以说是希尔伯特空间理论的幼年版，所以有时……

  …matrix inversion and the simplex algorithm of linear programming (optimization) and network linear programming. A good first text in linear algebra is by Ben Noble. The crown jewel is by Paul Halmos, 'Finite Dimensional Vector Spaces', written when Halmos was an assistant to von Neumann; the book approaches linear algebra much like it was functional analysis and, thus, is a baby version of Hilbert space theory and, thus, sometimes…

• lr1970 · 2021 年

  迄今为止，从向量空间和线性算子视角深入浅出讲解线性代数的最佳书籍，当属保罗·哈尔莫斯的《有限维向量空间》。举个例子，哈尔莫斯引入矩阵（或算子）行列式的方式，是我见过最自洽、最优雅、最简洁的。而在 Kenneth Kuttler 的线代书里，行列式……

  The best, by far, book on Linear Algebra that elegantly teaches it from Vector Spaces and Linear Operators point of view is Paul Halmos "Finite-Dimensional Vector Spaces" For instance, the way Halmos introduces the determinant of a matrix (or an operator) is the most consistent, elegant and simple way I ever encountered. OTOH, in Kenneth Kuttler's LinAlg books the determinant…

• Tainnor · 2020 年

  ……到底用不用范畴论的语言，完全取决于个人，但“标准的数学处理方式”本身就已经非常优美且引人入胜了（如果我想找点灵感，就会翻开手头哈尔莫斯的《有限维向量空间》，对于初学者来说这未必是最好的入门书，但对已经学过线性代数的人来说，写得真是太漂亮了）。

  …the language of category theory or not, is up to anyone, but the "standard mathematical treatment" is quite beautiful and intriguing already (if I want to feel inspired, I open up my copy of Halmos's "Finite Dimensional Vector Spaces", not necessarily the best introduction for someone who is new, but very beautifully written for someone who has already seen linear algebra).

• HilbertSpace · 2009 年

  ……关于椭圆的内容，还能用上复数。而且这门课也是泛函分析和希尔伯特空间的入门引导。你可以用任何一本畅销教材起步，但最终一定要读一下经典之作——哈尔莫斯的《有限维向量空间》。哈尔莫斯是在给冯·诺依曼当助手时写下这本书的，初衷就是把它作为希尔伯特空间的有限维入门介绍（当年冯·诺依曼还不得不向希尔伯特本人解释希尔伯特空间呢），事实上它确实做到了。它……

  …about ellipses and get to use complex numbers. Also the course is an introduction to functional analysis and Hilbert space. Use any popular book to get started but in the end cover the classic, Halmos, "Finite Dimensional Vector Spaces'. Halmos wrote this when he was an assistant to von Neumann and intended it to be a finite dimensional introduction to Hilbert space (which once von Neumann had to explain to Hilbert) which it is. It…

• graycat · 2016 年

  ……矩阵求逆。关于伪逆矩阵，挺有意思的内容，但特别是针对你的问题来说，以后大概率用不上了，可以跳过。然后如果有时间的话，快速过一遍经典之作——哈尔莫斯的《有限维向量空间》。写于1942年，当时哈尔莫斯刚在 J. Doob 门下拿到博士学位（比如《随机过程》，以及后来的《经典位势理论及其概率对应物》），刚刚露面……

  …matrix inversion. For pseudo-inverses, cute material, but, especially for your question, likely won't see it again and can skip it. Then if have some time, take a fast pass through the classic, Halmos, Finite Dimensional Vector Spaces. It was written in 1942 when Halmos had just gotten his Ph.D. under J. Doob (e.g., as in Stochastic Processes and, more recently, Classical Potential Theory and Its Probabilistic Counterpart) and showed up…

• lliiffee · 2011 年

  关于哈尔莫斯，这确实挺吓人的。这几天我碰巧在读《有限维向量空间》，虽然内容挺基础的，但哈尔莫斯显然极度厉害，而一想到居然还有人甩开他好几个档次，就觉得不可思议……

  About Halmos, that is quite scary. I happened to be reading "Finite-Dimensional Vector Spaces" the last few days and while the material is pretty elementary, Halmos is obviously very good, and the idea that there are people leagues ahead of him is amazing...

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