Linear Algebra Done Right (Undergraduate Texts in Mathematics) 3rd ed. 2015 Edition

I used this book in my second course in linear algebra, and I absolutely loved it.One of my biggest points of irritation in my first course in linear algebra was the fact that we first defined determinant as some unintuitive, computational nonsense and then defined eigenvalues from there. Judging off of the foreword, Axler essentially wrote this book so that students like myself could gain some peace of mind.The material is developed wonderfully, in my opinion -- it was much more intuitive than my first pass at linear algebra, and the problems within the book (at least those that my professor assigned) were commonly quite good. On top of that, it was one of the first math textbooks I've owned that I could legitimately sit down and read rather than, say, fall asleep or come away more confused than when I first started reading. The proofs are *mostly* quite readable, and Axler definitely has an enjoyable writing style. Whether it's the little surprises like getting to page 22 and seeing it labeled "~7pi" (there are other easter eggs of that variety, by the way) or writing an anecdote from the supreme court where one of the justices is caught up on the word "orthogonal" inside the chapter on inner products and norms (p. 174), he certainly does his best to make reading the book enjoyable.Apart from the material itself, though, as others have mentioned, the book is also just plain looks nice. I purchased a hardcover edition (which I believe may be the only style printed for the 3rd edition), and whether it's the outer cover or the typeset they use inside, everything just has a nice, colorful pop to it. Coming in at ~330 pages and ~6.5W x 9.5H x 0.8D inches, the book is also compact, an aspect that made carrying it to and from campus each day a trivial task.As a whole, I have essentially nothing but praise for this text. Some may have wanted a linear algebra text that's more computationally intensive, but I'd rather gain the conceptual understanding that Axler has to offer than manually row reduce or invert some arbitrary matrix any day. I absolutely don't want to sell my copy -- this text is one that I'm going to be happy to leave on my bookshelf and use as a reference whenever I find myself needing to freshen up on my linear algebra later in life.

I completed this book as an undergraduate introductory course to linear algebra and formal proofs. The lucid explanations make the book ideal for someone without a lot of mathematical background. It was a joy to read, and the exercises are usually accessible and assume no prior knowledge — only a small fraction of problems are very involved.But the material is mostly theoretically interesting, and does not cover many of the computational tricks in a normal linear algebra class — Gauss-Jordan elimination, a hugely important topic, is not even mentioned. There are so many other things missing, like calculations. You work more with operators and vector spaces than with matrices, and finishing this book won't help you understand the matrix terminology that's common in linear algebra. The book is more suited as a primer to a higher-level theoretical class, like operator theory, functional analysis, or modern algebra. It cannot be a prerequisite to practical/applied courses, like, say, statistics or machine learning. I feel like I've learned a lot after finishing the book, but I don't feel prepared for courses that require a 'working knowledge' of linear algebra.If you're at all interested in theoretical aspects of algebra or being gently introduced to good proofs, this book will appeal to you. I had never done theoretical math before, and this book was interesting and accessible.

Teaches Linear Algebra as an Algebra. It’s flavor is very Abstract Algebra light (and working oen will carry over to the other).It is not, by itself, always excellent at creating intuition. Doing the exercises is part of that. Geometrically... well, you’ll probably get plenty of that over the course of ... just existing in any semi-technical realm.Compared to, say, Strang’s excellent online intro course (not a fan of his book, but the lectures are great; opposite of axler) Strang os great at getting hands dirty with simple systems and developing strong, key intuitions. Axler takes those simple comprehensions and intuitions and elevates them to something more sublime and, potentially, much more powerful.Despite his harping about finite dimensional vector spaces early on, a large part of the material discusses Infinite dimensional vector spaces amd here is where LA really helps bring new intuitions.If you took Strang’s course you learn to approximate data using projections. If you read the correspondong section of Axler you come away having learned to approximate arbitrary functions in the infinite space of functions with some subset of your choosing. The inner product, abstractly defined, allows for almost arcanely powerful tasks.But, again, it’s an algebraist’s take on LA. That’s not for everyone.