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Where to start learning Linear Algebra?

Does anybody know of a good book in Linear Algebra for self study for a beginner? I look for a book with many exercises.

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marked as duplicate by Ayman Hourieh, rschwieb, Old John, Jennifer Dylan, Asaf Karagila Aug 31 '12 at 22:26

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Strang's book is very accessible and provides many examples with applications. –  Arkamis Aug 31 '12 at 16:04
+1 for "Introduction to Linear Algebra", by Gilbert Strang. –  chaohuang Aug 31 '12 at 16:15
For lots of exercises, "Theory and Problems of Linear Algebra" by Seymour Lipschutz, in the Schaum's Outline Series. –  Peter Phipps Aug 31 '12 at 16:42
Gilbert Strang. There is the book and the course including video lectures. Can't ask for more! –  user2468 Aug 31 '12 at 17:07
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4 Answers

A very nice introduction is

"Linear Algebra and Geometry"

by Kostrikin and Manin.

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Maybe you can try:



  • Finite-Dimensional Vector Spaces by P.R. Halmos
  • Linear Algebra Done Right by Sheldon Axler
  • Linear Algebra by Georgi E. Shilov
  • Linear Algebra (Undergraduate Texts in Mathematics) by Serge Lang
  • 3,000 Solved Problems in Linear Algebra, Seymour Lipschutz
  • Linear Algebra: Examples And Applications, Alain Robert

There are many other wonderful sites and books, but those are some ideas to get you going.

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Needs a $+$ Roman numeral i –  amWhy May 19 '13 at 0:49
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Apostol: Calculus is what I learned from.

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If it is your first look at linear algebra ever, it might be worth checking out the Khan academy camcasts http://www.khanacademy.org/math/linear-algebra. They are short, simple and very well explained.

Linear algebra done right is (aside from the slightly cocky name) an excellent and short undergrad textbook on linear algebra that (at least in my opinion) stands out compared to others because presents all the basics without relying on the less intuitive notion of determinants for the proofs (determinants are only introduced in the very end). http://linear.axler.net/

Lastly, for applications and real life (ish) motivation it might be worth checking out the first half of this course given by Stephen Boyd. He links linear algebra concepts to engineering type problems (GPS, load distribution in buildings...etc), efficient computation and basic optimisation problems. http://see.stanford.edu/see/courseinfo.aspx?coll=17005383-19c6-49ed-9497-2ba8bfcfe5f6

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