Best matrices books according to redditors

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.

J.F. Cornwell, Group theory in physics: an introduction (link)

W. Ludwig, Symmetries in physics: group theory applied to physical problems(link)

M. Tinkham, Group theory and quantum mechanics (link)

W.-K. Tung, Group theory in physics (link)

E.P. Wigner, Group theory and its applications to the quantum mechanics of atomic spectra (link1, link2)

N. Jeevanjee, An Introduction to Tensors and Group Theory for Physicists (link)

G. Costa, Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries (link)

B. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (link)

R. McWeeny, Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics)(link)

I have always struggled learning numerical analysis systematically. Could someone recommend books on Numerical Linear Algebra, Numerical Solutions to ODE's/PDE's, Numerical Analysis etc. that have good coding exercises, along with the necessary theory etc. The coding exercises should preferably be in Python, I suppose.


The best book on numerical linear algebra I have found matching this criteria is Watkins' Fundamentals of Matrix Computations, https://www.amazon.com/Fundamentals-Matrix-Computations-David-Watkins/dp/0470528338, but the exercises in Matlab.


Another book I seem to like is this physics book on Mathematica:


https://www.amazon.com/Introduction-Mathematica%C2%AE-Physicists-Graduate-Physics/dp/3319008935/ref=sr_1_3?keywords=physics+mathematica&qid=1557866324&s=books&sr=1-3-spell


In this case, project problems are derived from physical examples, making learning numerical methods worthwhile, I suppose.


So can someone recommend good books on the aforementioned topics that use Python etc. for project problems that have context as,as perhaps, applications.

I've just finished going through Brian Hall's Book. I'm just learning these things for the first time, so maybe I just don't have a lot to compare it to, but I thought it was fantastic.

I will say, it's fairly easy. I often times found myself wondering why he was bothering to spell out things in an explicit proof when it was obvious, but as a book I was learning from without lectures, this was actually a good feature. He goes quite slowly so there's time for a self-learning to digest things. I do realize some people find this to be a problem though.

Also he only treats matrix groups, which can be a little bit limiting.

Matrix Algebra Useful for Statistics

More a cookbook but very useful. Gives examples of where properties of matrices are useful in statistical context

There's a wealth of materials out there. Here's an open content HPC text i really like: http://pages.tacc.utexas.edu/~eijkhout/istc/istc.html

Watkisn is often referenced, I haven't read: https://www.amazon.com/Fundamentals-Matrix-Computations-David-Watkins/dp/0470528338

and some course notes: http://people.ds.cam.ac.uk/nmm1/arithmetic/na1.pdf

http://people.inf.ethz.ch/arbenz/ewp/Lnotes/

http://www.seas.ucla.edu/~vandenbe/103/

also, besides Strang, the most often recommended LA texts are Axler, Insel/Friedberg/Spence, Hoffman/Kunze, I think.

How about Matrices and linear transformations By Charles G. Cullen. It's a Dover book, so the price is right, and users on Amazon seem to like it. Cullen treats both the matrix-oriented and vector space-oriented points of view, so it might be more appealing to someone interested in applications. It's also quite a bit shorter than the ponderous, overpriced tomes of Lay and Friedberg.

It seems normal to me (in the book I am reading, Matrices and Linear Tranformationsby Charles Cullen.)

Agree on recommending David Lay's Linear Algebra book. Disagree that numerical methods are of special emphasis over and above pure theory.

Most linear models texts rely on just the theory.

Something else you might like is the matrix text by Bernstein which is possibly the only text I'd say that is more comprehensive than Harville.