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So, if you don't already know linear algebra like matrices, finding eigenvalues of matrices, diagonalization, etc., then you shouldn't use Axler.

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Fredrik

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One thing that's a bit weird about it is that it avoids using determinants most of the time.

You will find lots of comments about this book and others if you do a search in the forum.

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My background is fairly minimal when it comes to matrices, vector spaces, etc. (most of it is based on the Leonard susskind lectures on QM).

So before I begin the text, I should most likely obtain a solid understanding of linear equations, matrices and determinants, right?

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Fredrik

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I think you'll struggle a bit with Axler. This isn't a bad thing however. If you're struggling then the course is too easy.

My background is fairly minimal when it comes to matrices, vector spaces, etc. (most of it is based on the Leonard susskind lectures on QM).

So before I begin the text, I should most likely obtain a solid understanding of linear equations, matrices and determinants, right?

But I do recommend getting a text other than Axler that is easier. For example, Lang's "introduction to linear algebra" (and not "linear algebra") is a good text that is not too hard. It covers matrix manipulations in more detail than Axler, so it's worth to go through it.

So if you learn from both Lang and Axler, then you should be fine.

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Yes, that's for sure. The book is very theoretical. If you want a theoretical text, then Axler is one of the best choices you can make. Other choice are Roman (this is very advanced though, so I don't recommend it), Hoffman & Kunze, Shilov and Lang (both books).

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Okay thanks, I wanted to confirm that. And i'll look into your other recommendations.Yes, that's for sure. The book is very theoretical. If you want a theoretical text, then Axler is one of the best choices you can make. Other choice are Roman (this is very advanced though, so I don't recommend it), Hoffman & Kunze, Shilov and Lang (both books).

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mathwonk

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I like this book by Sergei Treil better than Axler's book. And it's free.

Actually I agree Axler's book is well written, but I think I agree with micromass that it may not be that helpful. Some books were written to prove a point, and others are actually useful to learn from. It is more important to get a feel for a topic at first rather than see slick proofs of the main theorems.

http://www.math.uga.edu/~roy/rev.lin.alg.pdf

Here is a book i wrote as an exercise over xmas break a while back, making the whole subject essentially a set of exercises for the reader. It is also free.

http://www.math.uga.edu/~roy/rev.lin.alg.pdf

(The same criticisms of Axler probably apply to mine too.)

I second the recommendation of Shilov, as both more thorough and cheaper than Axler.

https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20&tag=pfamazon01-20

There is no shame in starting on an easier book, also free, to see if it is helpful.

http://joshua.smcvt.edu/linearalgebra/

Here is another nice gentle introduction by a Stanford professor:

http://www.abebooks.com/servlet/SearchResults?an=paul+shields&sts=t

If you like to challenge yourself you might try to read and provide the proofs in my 15 page book above, and when stuck on a page, read the 20-30 pages of one of the more standard books where the same result is discussed. I made up many of my proofs though, so they probably won't resemble the ones in other books.

Lang is very clear on the main ideas but he essentially never gives enough examples in his books for the reader to really master the subject well, so books by Lang always need supplementation.

Actually I agree Axler's book is well written, but I think I agree with micromass that it may not be that helpful. Some books were written to prove a point, and others are actually useful to learn from. It is more important to get a feel for a topic at first rather than see slick proofs of the main theorems.

http://www.math.uga.edu/~roy/rev.lin.alg.pdf

Here is a book i wrote as an exercise over xmas break a while back, making the whole subject essentially a set of exercises for the reader. It is also free.

http://www.math.uga.edu/~roy/rev.lin.alg.pdf

(The same criticisms of Axler probably apply to mine too.)

I second the recommendation of Shilov, as both more thorough and cheaper than Axler.

https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20&tag=pfamazon01-20

There is no shame in starting on an easier book, also free, to see if it is helpful.

http://joshua.smcvt.edu/linearalgebra/

Here is another nice gentle introduction by a Stanford professor:

http://www.abebooks.com/servlet/SearchResults?an=paul+shields&sts=t

If you like to challenge yourself you might try to read and provide the proofs in my 15 page book above, and when stuck on a page, read the 20-30 pages of one of the more standard books where the same result is discussed. I made up many of my proofs though, so they probably won't resemble the ones in other books.

Lang is very clear on the main ideas but he essentially never gives enough examples in his books for the reader to really master the subject well, so books by Lang always need supplementation.

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For first texts, you might try:

Anton - "Elementary Linear Algebra"

Strang - "Linear Algebra and its Applications"

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Fredrik

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