Linear Algebra Done Right
by Sheldon Jay Axler · first published 2004
73% recommend23% neutral4% critical
Why HN recommends it
A proof-based, coordinate-free treatment that delays determinants until motivated, building real understanding of eigenvectors, null spaces and abstract vector spaces. For readers moving past rote matrix computation.
Common criticism: Too abstract and deep-end for first-time learners
Summarised by Claude from recommending comments
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It's nice to have a free book as a supplement. Linear Algebra Done Right by Sheldon Axler is a much better choice and when making an investment in learning, particularly a difficult subject like linear algebra, saving money with a free text is probably the most expensive thing…
on “Linear Algebra by Jim Hefferon – free textbook” ↗…not a difficult book but is very abstract and rigorous so makes a good introduction. If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh. Other good books are Linear Algebra Done Right by Axler, or the linear algebra book by Friedberg, Insel, and Spence. Maybe even learn linear algebra first. It's so useful. Do plenty of exercises in every chapter, and read carefully. Count on about…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗I found Linear Algebra Done Right by Axler to be a fantastic theoretical text that makes everything click together from day 1. It's derived from his paper Down with Determinants. He starts by explaining that linear algebra is about studying…
on “An Intuitive Guide to Linear Algebra” ↗"Linear Algebra Done Right" https://linear.axler.net/ There's a compact and free form on the book on that page.
on “Calculus Made Easy (1910)” ↗…rush through it, but to expand your mind through each problem. Step 4: Pick any of these books that interest you the most and do the same: - Calculus by Spivak - Algebra: Chapter 0 by Paolo Aluffi - Linear Algebra Done Right by Axler By then you should have enough mathematical maturity to know what to do next.
on “Mathematicians are chronically lost and confused (2014)” ↗This is why I'm a big fan of Axler's Linear Algebra Done Right. The book's emphasis is on the concepts behind the calculations rather than the calculations. I actually disagree with Axler on his avoidance of the determinant, though. I wish instead of avoiding it…
on “Matrix Multiplication” ↗Axler seems to have won that battle. His textbook Linear Algebra Done Right is widely used at 308 universities including Berkeley, Stanford and MIT. He has a PDF available without proofs, videos, etc. 3blue1brown likes the book. http://linear.axler.net/ I suffered through determinants.
on “Down with Determinants (1995)” ↗I think the book you're talking about is Axler's "Linear Algebra Done Right." I worked through the problems in this book with some friends, and it is a very good presentation. After doing that book I wanted to see what other books were out there, which ones were the good ones,…
on “Fundamentals of Linear Algebra and Optimization [pdf]” ↗…intuitions while picking up the mathematical ones. The drawback is that you have to make sure you're not cheating yourself of the mathematics by over-relying on the geometry. Sheldon Axler's acclaimed "Linear Algebra Done Right" is freely available as a download [1] through July due to the pandemic. I've not read it (yet!), but I've heard so many good things about it I feel comfortable recommending it off the cuff. :) (Recommendation:…
on “Ask HN: What are you learning?” ↗…operations, that you can come away believing that linear algebra is somehow _about_ matrices and their operations. I know many in my university class seemed to believe that. A book I enjoyed is Axler's Linear Algebra Done Right[0], in which, if I remember correctly, doesn't contain a single matrix. [0]https://zhangyk8.github.io/teaching/file_spring2018/linear_a...
on “A 2020 Vision of Linear Algebra” ↗Axler's Linear Algebra Done Right has always been my favorite linear algebra text (I say this 10+ years after reading it and finishing my math PhD, if that matters). For those who want a free alternative, behold: Treil's Linear Algebra…
on “Linear Algebra by Jim Hefferon – free textbook” ↗I've read and would recommend Linear Algebra Done Right by Sheldon Axler. http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/... For numerical aspects of linear algebra (and other subjects), I've found Numerical Recipes to be quite helpful.
on “Surprises from numerical linear algebra (2010)” ↗…defining a vector space, and then it jumps into determinants. IMO this is the wrong way to understand linear algebra, and the typical path of a lot of introductory text books. A better text: Axler's "Linear Algebra Done Right"
on “A First Course in Linear Algebra” ↗Sheldon Axler's "Linear Algebra Done Right" has my highest recommendation if you want expertise in linear algebra. As a followup, Paolo Aluffi's "Algebra: Chapter Zero" is the best synthesizing text for abstract algebra for a beginning graduate…
on “Ask HN: Math books like SICP?” ↗Without getting bewildered I would suggested going through these 3: 1. Book of Proof by Hammack (http://www.people.vcu.edu/~rhammack/BookOfProof/) 2. Calculus by Spivak 3. Linear Algebra Done Right by Axler Be prepared to work through all (or at the very least only the odd numbered) exercises. If you can't stomach that or find that life gets in the way of you completing even these very basic books,…
on “Foundations of Data Science [pdf]” ↗