线性与几何代数
Linear and Geometric Algebra
Alan Macdonald · 初版 2011 年
14人推荐
20位读者提及
27次提及
为什么值得读
- 配套习题适合用来系统自学几何代数
- 同时讲授传统矩阵代数与几何代数基础
- 附带视频资源辅助攻克抽象数学概念
这本适用于本科第一门线性代数课程的教材，在涵盖常规线性代数大部分主题的同时，对线性代数与几何代数进行了统一阐述。几何代数是线性代数的自然延伸，它深化并增强了对诸多线性代数论题的处理方式。不仅如此，几何代数还能发挥更深远的作用。几何代数及其拓展出的几何微积分，将涉及几何思想的广阔数学领域统一、简化并加以推广。它们为物理学、计算机科学以及其他诸多领域提供了一门统一的数学语言。
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我很庆幸自己读过的书：《网球内功心理学》（The Inner Game of Tennis） Keith Johnstone 写的《即兴》（Impro） 《看见国家》（Seeing Like a State） 《建筑的永恒之道》（The Timeless Way of Building） Alan Macdonald 写的《线性与几何代数》（Linear and Geometric Algebra） 马可·奥勒留的《沉思录》（读过三遍） 《小熊维尼之道》（The Tao of Pooh） 《科学、战略与战争：约翰·博伊德的战略理论》（Science, Strategy and War） 《天才儿童的戏剧》（The Drama of the Gifted Child） 《互动仪式……
Books I'm glad I've read: The Inner Game of Tennis Impro by Keith Johnstone Seeing Like a State The Timeless Way of Building Linear and Geometric Algebra by Alan Macdonald Meditations by Marcus Aurelius (read this one thrice) The Tao of Pooh Science, Strategy and War: The Strategic Theory of John Boyd The Drama of the Gifted Child Interaction Ritual…
……Google 搜索“克利福德代数”（Clifford Algebra）。如果你想要一本试图同时讲解几何代数和传统矩阵代数的本科入门教材，可以看看 MacDonald 的《线性与几何代数》（Linear and Geometric Algebra）；我觉得 Hestenes 并不太认同这种路子，但针对类似读者群体的教材实在不多。MacDonald 还写过一本《向量与几何微积分》（Vector and Geometric Calculus），它……
…google search for “Clifford Algebra”. If you want an introductory undergraduate textbook which tries to teach both geometric algebra and traditional matrix algebra, you could look at [MacDonald][]’s [Linear and Geometric Algebra][laga]; I don’t think Hestenes is really on board with this approach, but there’s not too much else pitched at a similar audience. MacDonald also has a book [Vector and Geometric Calculus][vagc] which…
对于想学几何代数（geometric algebra）的人，我强烈推荐 Macdonald 写的《线性与几何代数》（Linear And Geometric Algebra）。我全靠这本书自学了这个课题（确保刷完了所有习题），而且甚至很享受这个过程！有点不可思议的是，这套代数后来在工作中居然派上了用场……
For those who want to learn geometric algebra I strongly recommend Linear And Geometric Algebra by Macdonald. I taught myself this subject entirely from this book (making sure I did all the exercises) and even enjoyed the process! Slightly weirdly an application of the algebra became useful at work…
顺便分享另一个资源，Alan Macdonald 录制了一些很棒的视频来配合他的书《线性与几何代数》和《向量与几何微积分》：https://www.youtube.com/channel/UCymE67THrWoeTABxzJm1wdg/pla...
For another resource, Alan Macdonald has some nice videos that accompany his books, "Linear and Geometric Algebra" and "Vector and Geometric Calculus": https://www.youtube.com/channel/UCymE67THrWoeTABxzJm1wdg/pla...
……在我搞明白之前，我没觉得那些视频有哪个特别管用。同理，我现在依然觉得四元数的那些视频没多大用。我觉得有些课程讲义挺有用 [0]。然后我硬啃了 Alan MacDonald 写的《线性与几何代数》（Linear and Geometric Algebra）。简而言之，别放弃。你可以通过最曲折的路径最终理解这些知识，而且这样你的理解反而会深刻得多。如果你真打算硬啃，这里有一个我用惨痛教训换来的小建议……
…found any of the videos particularly useful before I understood. Likewise, I still don't find any of the quaternion videos too useful. I found some course notes to be useful [0]. I then worked through "Linear and Geometric Algebra" by Alan MacDonald. In short, don't give up. You can come to understand things by the most indirect of paths and your understanding will be all the better for it. One hard-learnt tip if you do choose…
我要安利一下 Alan Macdonald 的《线性与几何代数》（Linear and Geometric Algebra）这本书，它能帮你很好地建立直觉，搞懂这篇博文后半部分的内容。
I'm going to plug Alan Macdonald's Linear and Geometric Algebra book as a great way to get an intuitive grip on the latter parts of this blog post