Reddit Reddit reviews Elementary Linear Algebra

We found 2 Reddit comments about Elementary Linear Algebra. Here are the top ones, ranked by their Reddit score.

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2 Reddit comments about Elementary Linear Algebra:

u/clarinetist001 · 12 pointsr/statistics

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.
u/anon35202 · 7 pointsr/3Blue1Brown

I can give you a counter-example. What book NOT to buy:

https://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/1133110878

The introductory quote from the first linear algebra video from 3Blue1Brown is:

"There is hardly any theory which is more elementary than linear algebra, in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices."

  • John Dieudonne

    The textual abuse and systematic obfuscation of such simple concepts as linear algebra is perfectly captured in that textbook.


    Browsing around I found this:

    https://math.stackexchange.com/questions/160056/what-is-a-good-book-to-study-linear-algebra

    and then this:

    http://math.mit.edu/~gs/linearalgebra/

    Which looks better. The problem with Linear Algebra is that it's taught by people with their heads stuck in the clouds in their crystal fortresses where they already know the problems, know the questions, know the procedures, and they've completely forgotten what it means to not know anything about linear algebra. So teaching it is reduced to repetitive procedure, endless transforming of matrices that might as well be these intricate recipes that turn unsatisfying mysterious symbols into other unsatisfying mysterious symbols.

    It's a subject ripe for disruption, ready for a completely different approach where we go back to first principles where we go back to the reasons for why the people who created linear algebra did what they did, and then follow their footsteps. It's just math around lines. It's easy to get lost in the steps of the recipe that you don't see the point. That in this 3d realm there are imaginary things called lines, and we can perform mathematical operations on those lines in order to do things like for example figure out how to calculate distance between lens and object in view when all we know is distance between fovea and lens, and the angle and distance between edges on rods/cones.

    The point of linear algebra is to reduce the miracle of complex things like rays of light, and how our eyes achieve vision into equations that can be processed by a computer so we can teach a computer to see like humans do. Light is just lines.