A good book for a second year linear algebra course?

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Just wondering if anyone can recommend a good linear algebra book for a second year course. In my first semester I learned up to Gram Schmidt process..EigenValues/Vectors etc. I don't care too much about how "easy" the book is to read. A book heavy in theory will do nicely if that's what you have in mind.
 

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  • #3
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If your first course was rigorous, try Advanced Linear Algebra by Roman. If not, check out Axler, Hoffman & Kunze, and Friedberg. Best of luck.
 
  • #4
mathwonk
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Here are my notes from a summer course I taught a while back, meant as a second linear algebra course. Our text for the course was officially Friedberg, Insel, and Spence, which I thought was good. My approach differs from theirs mainly in my extensive use of the concept of the minimal polynomial of a linear map, as an organizing principle. For some reason Insel, et al. seemed the feel that using polynomials made the course too advanced. I also used Shilov as a supplementary text.

Obviously I am not qualified to call my book good, but it is free. Objectively I would say it probably lacks sufficient examples and problems, but overall I enjoyed learning and explaining the ideas while writing it.
 

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  • #5
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Check this: https://www.physicsforums.com/blog.php?b=3206 [Broken]

I think Hoffman and Kunze would be an ideal book for you.
 
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  • #6
mathwonk
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I agree with the other recommendations here under the rubric "good". I just offered mine because its free. Hoffman and Kunze especially is a classic, (but sometimes pricy).

Here is a reasonable one though, used:

http://www.biblio.com/search.php?author=hoffman,+kunze&title=&keyisbn=&format=&dealer_id=133308

LINEAR ALGEBRA
Kunze, Ray & Hoffman, Kenneth
Bookseller: Samkat Books
(Dyersburg, TN, U.S.A.)
Bookseller Rating:
Quantity Available: 1

Price: US$ 22.50
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Book Description: Prentice-Hall, Englewood Cliffs, N. J., 1961. Hardcover. Book Condition: Ex-Library; G/NONE. Not Latest Edition. Moderate edge wear. Previous owner's name marked out inside front cover. Pages clean, binding good. ; 332 pages. Bookseller Inventory # 63391
 
  • #7
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either Linear Algebra Done Right (which is the Axler everybody is talking about)

or if you have an ok background in group theory, then I'd say go for Advanced Linear Algebra (again, people have already recommended this one, it's by Steven Roman)

the later is a little more robust, as it is intended for graduate students in mathematics, where the former is intended for upper level undergraduates.

An additional one I thought about that might work for you if you want a short, free text to be a bridge between where you are now and then picking up Roman's book:

http://www.math.miami.edu/~ec/book/

It's free to download the whole thing and it focuses on learning the algebra necessary to get into a more in depth exploration of linear algebra.
 
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  • #8
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Hey thanks so much for the quick replies

I'm currently browsing through the books suggested here and I'm leaning towards getting both Axler and Roman or Roman and Kunze, Ray &Hoffman, Kenneth. It seems Roman is the more rigorous book choice and If I get lost going through that I'll fall back on Axler and the free texts listed here. MathWonk and bpatrick thanks so much for the links to the free texts..MathWonk Ill check out your's out as soon as the pdf is approved and the link is available :)
 
  • #10
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I prefer Shilov over Axler or Hoffman & Kunze.
 
  • #11
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MathWonk Thanks for the links! I was looking through your book and the material seems to be within my grasp which is good news..I think
 

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