Second Book on Linear Algebra

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Hello folks,

I am currently finishing up a class on linear algebra, covering vector spaces, bases and dimension, geometry of n-dimensional space, linear transformations and systems of linear equations. I am only getting accustomed to proof writing for the first time in this course. However, I am enjoying the material and the problems, and would like to study more. I am wondering what a good second text would be? The options have considered so far are Axler, Friedberg/Insel, Hoffman/Kunze. Which text is the more gentle one? I will be self studying until they offer the second course, probably next year. Any ideas would be helpful.

Thanks,
MM
 

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  • #3
Infrared
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I'm only familiar with Axler but I think it should be suitable for you. It's rigorous, but pretty gentle and good if you're just getting started with proof-based mathematics. Just make sure you do plenty of exercises.

One idiosyncrasy of Axler is his aversion to determinants. He does as much as he can without determinants (including a nice argument for the existence of eigenvalues) and doesn't even define them until the end of the book iirc, so you should probably find another source to read about them.
 
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  • #4
mathwonk
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Of those three, Friedberg-Insel is the most gentle, with the most explanations and examples. Hoffman Kunze is the most abstract probably, but more detailed than Axler. For self study I would recommend Friedberg and Insel, although Treil is also excellent.
 
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I think I'll work through Friedberg first, then check out the others. I'm a physics student still getting acquainted with proofs. It's fun, but it's not easy.

I also have Linear Algebra and Group Theory by Smirnov, and A Vector Space Approach to Geometry by Hausner. Both look fun.
 
  • #7
mathwonk
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here also is a free set of notes from one of my summer courses in the subject, meant as a second course. they are so short, some 70 pages, that they cannot be that gentle. but they may offer some insights just by reading the statements of the theorems as opposed to the proofs, and some of the possibly smart alecky comments. There are also three or four other linear algebra note sets on that same webpage.

oh, and I love smirnov's book on linear algebra, sooo clear. it was a reference in my course.

http://alpha.math.uga.edu/~roy/4050sum08.pdf
 
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