Linear Algebra by Jim Hefferon – free textbook
What is nice about this book is it includes solutions to exercises. I wish more proof-theoretic books included exercises in the back of the book like this one does. Yes, you can prove something in multiple ways, and no that isn&#x27;t a good excuse to not include at least one version of the proof in the back of the book. It really benefits the self-learner. The math community seems to have a lot of artificial gatekeeping to keep non-academics out.<p>They do this in several ways.<p>1) They recommend textbooks to beginners that are too advanced for their skill level.<p>2) These textbooks do not include solutions and the advice given is that solutions would somehow rob them of the experience (don&#x27;t let those that lack self-discipline ruin learning for non-traditional students that aren&#x27;t in a formal classroom with access to professors and TAs). The self-learner needs some sort of feedback system.<p>3) They tell the self-learner that solutions aren&#x27;t provided because everyone has the ability to know if their solutions are correct without having their work checked. Would you write a complicated program and write no test cases, or could you instantly know your program is bug free the first time you write it? Why is math suddenly any different?<p>Despite popular elitist opinions, I&#x27;d recommend this book over Axler for the beginner that doesn&#x27;t know linear algebra. Everyone says Axler is the perfect first book in linear algebra. It really isn&#x27;t. Even Axler admits this himself in the preface. He assumes that it is a second approach to the field.<p>But people like to be elitist and recommend books to beginners that aren&#x27;t always best from a pedagogical  perspective.<p>Those are the same class of people that recommend Rudin or Spivak to someone that wants to study elementary calculus 1 material.