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I am looking for good graduate linear algebra books that contain practice problems with solutions (which is better) or hints to solve the problems. By the way, two graduate courses I am gonna take are a continuation of the undergrad course I have already taken based on the textbook: "Linear Algebra: A modern Approach" by "D.Poole". I did find some textbooks that cover the material, like: "Linear Algebra done right", "Linear Algebra done wrong", etc and some of these books suggest few problems without given solutions. So, I need books with many solved problems (or hints) that help me to practice what I will learn in the lecture and to ensure I well understand the material. Any suggestion is more than welcome. Thanks

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Graduate? Hmm... well, perhaps you should look at abstract algebra books. Dummit & Foot, "Abstract Algebra" is good. Lang's "Algebra" is rather dense, and is not for the faint of heart, but if you're adventurous enough (or after reading a softer introduction first), it is excellent for its rigor and hard problems (I remember studying that for my Algebra qualifying exam). –  William Jan 8 '12 at 18:06
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Halmos's Linear algebra problem book is worth checking out. –  Jonas Meyer Jan 8 '12 at 18:51
    
I like Hefferon, joshua.smcvt.edu/linearalgebra , and it has the advantage that it's free. The answers to the exercises are available. –  Ben Crowell Jan 8 '12 at 18:59
    
As for practice problems, I'm not sure, but I have a special place in my heart for Curtis' Abstract Linear Algebra. It's a tiny little book which is so easy to read. –  Bill Cook Jan 8 '12 at 21:58
    
Also Viktor Prasolov, " Problems and theorems in linear algebra " –  WLOG Jan 8 '12 at 22:45
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7 Answers 7

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There's a book by Jonathan Golan called The Linear Algebra a Beginning Graduate Student Ought to Know. I would take look at that. It has tons of pretty good problems.

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Linear Algebra Done Right is a key text at Harvard, MIT, and Berkeley. So, despite some attitude issues (starting with the title) it might be worthwhile to give it your fullest consideration.

Here is a link to course materials generously made available at MIT which has all you need, including a set of great lecture beamers.

http://math.mit.edu/~trasched/18.700.f11/index.html

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My favorite linear algebra book is "Linear Algebra" by Hoffman and Kunze. I absolutely love it, and recommend it.

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Does this book contain problems with solutions really? –  the symplectic camel Jan 14 '12 at 13:46
    
It has numerous worked examples, and problem sets to go along with them... If you mean a solutions manual I don't know... –  kηives Jan 14 '12 at 18:29
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I would like to recommend "Linear algebra: challenging problems for students" by Fuzhen Zhang

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In addition to the Halmos book already mentioned, which is indeed excellent, there are several other problem books/solution manuals for theoretical linear algebra:

  1. Shakarchi's Solution Manual to Lang's Linear Algebra

  2. Blythe's Algebra Through Practice: Matrices and Vector Spaces and Algebra Through Practice: Linear Algebra

  3. Don't overlook Schaum's outline of linear algebra. There are some good problems in there as well

Also, I would find it somewhat surprising if you couldn't find solutions to many of Axler's problems on-line.

Added:

One very good sources of problems/solutions that I neglected to mention is UC Denver's archive of past Applied Linear Algebra qualifying exams (with solutions) found here: Qualifying Exams. Don't be misled by the adjective "applied"; these problems are theoretical in nature and a similar to those found in Axler (though perhaps a little more demanding, but not by much)

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the Halmos book and Blythe's book are good reference but it is elementary book in linear algebra.I suggest you Linear Algebra by Stephen H. Friedberg or Problems and Theorems in Linear Algebra by V. V. Prasolov

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I would argue that the books by both Blythe and Halmos are roughly on the same level as the Axler text to which the OP refers. –  ItsNotObvious Jan 13 '12 at 15:11
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In Berkeley Problems in Mathematics book, there are a lot of problems with solutions of Linear Algebra as well as Analysis and Algebra. The problems are taken from Preliminary Exams of UC Berkeley.

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