Linear and Geometric Algebra
by Alan Macdonald · first published 2011
70% recommend20% neutral10% critical
Why HN recommends it
Undergraduate-level introduction that presents linear algebra geometrically and carries it through to geometric algebra. Self-learners value its exercises and the intuition it builds for vector spaces.
Summarised by Claude from recommending comments
This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields.
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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…
on “Ask HN: Books you read in 2015?” ↗…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…
on “Clifford Algebra: A visual introduction (2014)” ↗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…
on “A Unified Mathematical Language for Physics and Engineering (1996) [pdf]” ↗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...
on “How Quaternions encode rotations: derivation and sample code” ↗…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…
on “Visualizing quaternions: An explorable video series” ↗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
on “Euclidean Spaces” ↗Linear and geometric algebra Vector and geometric calculus Both by Alan macdonald, both very good.
on “Seven-Dimensional Cross Product” ↗In addition to gibsonf1's recommendations (not books), the following books are good. The first 2 are more pure introductions to the math, the third is applying it to physics, the fourth to CS. Linear and Geometric Algebra, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/laga/ Vector and Geometric Calculus, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/vagc/index.html Application to physics: New…
on “Introduction to Clifford Algebra (2006)” ↗Macdonald's Linear and Geometric Algebra is an excellent GA text which not only geometrically derives complex numbers (and rotation via their exponentiation), but also quaternions.
on “How imaginary numbers were invented [video]” ↗…good beginner source, but I haven’t ever really sat down and tried to go comprehensively through the exercises in any books pitched at a relatively elementary level. You could try Alan MacDonald’s book Linear and Geometric Algebra which is designed as an intro undergraduate textbook. If you want to also learn some mechanics, you could try Hestenes’s book New Foundations for Classical Mechanics.
on “Symplectic Geometry in 2D – Points, Lines, Circles” ↗"Linear and Geometric Algebra" by Alan Macdonald. It's definitely not the norm compared to many of the other listings in this thread but it definitely gave me a better understanding of many algebraic properties and helped build an…
on “Ask HN: Best beginner friendly linear algebra book?” ↗Linear and Geometric Algebra, by Alan MacDonald. http://www.faculty.luther.edu/~macdonal/laga/ It's a great and very geometric presentation of linear algebra that takes it through to geometric algebra. A very nice presentation…
on “Ask HN: Best beginner friendly linear algebra book?” ↗Thanks for the detailed answer. I have previously studied a bit from "Linear and Geometric Algebra" by Alan Macdonald (nice book) but I don't have any Physics background. I'm interested in learning more, however!
on “A Swift intro to Geometric Algebra” ↗Have you seen Macdonald's "Linear and Geometric Algebra"? I found it a much nicer introduction to the subject.
on “Linear Algebra Done Right – 4th Edition” ↗…Immersive Linear Algebra, https://immersivemath.com/ila/index.html (online book) - Margalit et al., Interactive Linear Algebra, https://textbooks.math.gatech.edu/ila/ (online textbook) - Macdonald A., Linear and Geometric Algebra - Macdonald A., Vector and Geometric Calculus - Ramirez et al., From Vectors to Geometric Algebra, 2018, https://doi.org/10.48550/arXiv.1802.08153 - Hertzmann et al., Computer Graphics Lecture…
on “Tell HN: Comp Sci, Algebra and Calculus Resources I Like” ↗