Reddit reviews Elementary Linear Algebra

I have a B.S. in mathematics, statistics emphasis - and am currently in the second semester of Linear Models in a M.S. Statistics program.

Contrary to popular opinion, I don't think Linear Algebra Done Right is suitable for learning linear algebra. Statistics - as far as I've gathered - is more focused on what is called "numerical linear algebra," rather than the more algebraic (and more abstract) approach that Axler takes.

It took a lot of research on my part to find better books. I personally believe that these resources are much better for covering the linear algebra needed for linear models (I recommend these after a first-course treatment in linear algebra):

• Linear Algebra Done Wrong, Treil (funny title, hm?). I would recommend focusing on all of Ch. 1, all of Ch. 2 (skip 2.8), Ch. 3.1 through 3.5, all of Ch. 4, Ch. 5.1 through 5.4 (5.4 is extremely important). The only disadvantage of this book is that it isn't specifically geared toward statistics.
  
  
• Matrix Algebra by Gentle. Does not cover proofs, but it is a nice catalog of methods and ideas you should know for a stats program. Chapters 1 through 3 are essential material. Depending on the math prerequisites demanded, chapter 4 is nice to know. I would also recommend 5.8, 5.9, 6.7, 6.8, and 7.7. Chapters 8.2 - 8.5 are essential material, along with 9.1 - 9.2. This includes the linear model material as well that you will find in a M.S. program. All of the other stuff is optional or minimally covered in a stats program, as far as I know.
  
  
• Matrix Algebra From a Statistican's Perspective by Harville. This does not cover any of the linear model material itself, but rather the matrix algebra behind it. It is the most complete book I have found so far on linear algebra for statistics. For the most part, you should know Chapters 1 through 14, 16-18, 20, and 21.
  
  I have also heard that Matrix Algebra Useful for Statistics by Searle is good, but I haven't read it yet.
  
  If you feel like your linear algebra is particularly strong (i.e., you're comfortable with vector spaces, matrix operations, eigenvalues), you could try diving right into linear models. My personal favorite is Plane Answers to Complex Questions by Christensen. I reviewed this book on Amazon:
  
  >It's a decent text. If you want to understand any part of this text, you need to have at least a first course in linear algebra covering matrices and vector spaces, some probability, and some "mathematical maturity."
  
  >READ THE APPENDICES before you read any part of this text. READ THE APPENDICES. Take good notes on them and learn the appendices well. Then proceed to Chapter 1.
  
  >Definitely one of the most readable books I've read, but it does take a long time to digest everything. If you don't have a teacher to take you through this material and you're completely new to it, you will find that some details are omitted, but these details aren't complicated enough that someone with an undergraduate degree in math wouldn't be able to figure them out.
  
  >Highly recommended. The only thing I don't like about this text is some of its notation. It uses Cov(A) to mean the variance-covariance matrix of a random vector A, and Cov(A, B) to mean E[(A-E[A])(B-E[B])^transpose ]. I prefer using Var(A) for the former case. Furthermore, it uses ' instead of T to denote the transpose of a matrix.
  
  No linear models text will cover all of the linear algebra used, however. If you get a linear models text, you should get your hands on one of the above linear algebra texts as well.
  
  If you need a first course's treatment in Linear Algebra, I prefer [Linear Algebra and Its Applications](http://www.amazon.com/Linear-Algebra-Its-Applications-Edition/dp/0201709708) by Lay. The 3rd edition will suffice, although I think it's in the 5th edition now. Larson's [Elementary Linear Algebra*](http://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/1133110878/ref=sr_1_1?s=books&ie=UTF8&qid=1458047961&sr=1-1&keywords=larson+linear+algebra) is also a decent text; older editions are likely cheaper, but will likely give you a similar treatment as well, so you may want to look into these too. I learned from the 6th edition in my undergrad.

Learning Calculus prior would be helpful, but probably not necessary. I'd recommend getting a Linear Algebra book and start working through it. I used this one in my university Linear Algebra course and it is fairly well written, and approachable. You can probably find this book online as a pdf somewhere.

Elementary Linear Algebra by Larson, Edwards and Falvo.

Amazon link here.

I used a book by Larson and Falvo called Elementary Linear Algebra. So far the book was really good at explaining every topic.

I had a stellar professor and a great book. I thought it was a breeze. I used this book in undergrad: http://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/0618783768/ref=sr_1_25?ie=UTF8&qid=1421682001&sr=8-25&keywords=linear+algebra

As far as notation: it will change from book to book. Learn as you go. I certainly didn't have a class or a book dedicated to the notation of mathematics. Generally the author will briefly explain their notation as they introduce the topic.