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I am a software developer who self study maths as my hobby, I have had taken a linear algebra course in my undergraduate/graduate study, but you know, math books written in China are such a rubbish that I just throw them away. So I want to buy some renowned textbook on linear algebra for me to study. I skimmed through amazon.com and google for "best book on linear algebra" , but there is no unanimous acknowledged textbook to linear algebra as "Thomas calculus" to calculus. I got some candidates:

"Introduction to Linear Algebra" by Gilbert Strang

"Linear Algebra and Its Applications" by Gilbert Strang

"Linear Algebra: A Modern Introduction" by David Poole

"Linear Algebra (2nd Edition)" by Kenneth M Hoffman and Ray Kunze

But from comments following them, each has its pros and cons, so as a beginner on this topic, can anyone give me suggestion about which book to choose? Thank you.

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I started learning linear algebra in my Undergraduate days from Linear Algebra (2nd Edition)" by Kenneth M Hoffman and Ray Kunze. I recommend this. –  zapkm May 30 '12 at 8:16
    
Does this book has a solution manual available? I want to check my answers or get some inspirations on difficult problems. –  wangshuaijie May 30 '12 at 8:20
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This, I think, is off-topic for MathOverflow (please see our FAQ). Before you ask at math.stackexchange.com , please see if any of the following answers your question: math.stackexchange.com/q/143904/1543 math.stackexchange.com/q/79674/1543 math.stackexchange.com/q/43930/1543 math.stackexchange.com/q/149666/1543 math.stackexchange.com/q/101994/1543 math.stackexchange.com/q/87362/1543 –  Willie Wong May 30 '12 at 8:37
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furthermore, it may actually also be a duplicate of mathoverflow.net/questions/16994/linear-algebra-texts –  Willie Wong May 30 '12 at 8:38
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I will happily second these three suggestions. Halmos book was my introduction to Linear Algebra and I loved it.--- Dick Palais –  Dick Palais May 31 '12 at 23:15
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1 Answer

up vote 2 down vote accepted

Strang and Kunze&Hoffman are good choices. You can also take up Halmos's Finite Dimensional Vector Spaces for a more abstract approach.

As for solutions, I would be actually a bit wary of a mathematical textbook that includes them. Most good ones don't (but not all, one notable exception is Spivak's fantastic Calculus that has solutions to half of the exercises). Think about it, the textbook is there to teach you the concepts, to motivate them and to give examples, it's not there to drill you. If you were enrolled in the course, the drill part would be handled in tutorials and hws; as a self-learner you can hardly do better drillwise than getting a Schaum's.

Best of luck!

EDIT: For advanced problems there are two wonderful and perhaps less-known books (at least I haven't seem them mentioned at all in the thread Vladimir linked to) are:

Linear Algebra: Challenging Problems for Students by Fuzhen Zhang

and

Linear Algebra Problem Book by Halmos

As a student, I had learned a lot from them.

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I wholeheartedly agree that "Linear Algebra Problem Book" is wonderful. In fact, I rather meant it than "Finite Dimensional Vector Spaces" in my comment to the original post. –  Vladimir Dotsenko May 30 '12 at 9:51
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