How to self study Linear Algebra

Solution 1:

First, bravo to you for taking initiative and immersing yourself in the beauty of learning!

Here are some thoughts for your consideration:

1. Elementary Linear Algebra [Hardcover] Ron Larson (Author)

2. Schaum's Outline of Linear Algebra Seymour Lipschutz (Author), Marc Lipson (Author)

3. Also, try your local university library and see if you find books that suit your needs.

You can also try open course-ware like:

1. http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-1-the-geometry-of-linear-equations/

2. http://www.khanacademy.org/math/linear-algebra

3. http://cnx.org/content/search?words=linear+algebra&allterms=weakAND&search=Search&subject=

I would also recommend you learn a Computer Algebra System (CAS) like Mathematica or Maple (you can purchase Student Versions) or other free ones (like SAGE or Maxima) because that will really help exploring and learning this topic so much richer!

See: http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

Lastly, I think you should consider learning proofing methods and here are some books that do a reasonable job at teaching those.

General Proof Strategies

1. How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) [Paperback] G. Polya (Author)

2. How to Prove It: A Structured Approach [Paperback] Daniel J. Velleman (Author)

3. The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs [Paperback] Antonella Cupillari (Author)

4. How to Read and Do Proofs: An Introduction to Mathematical Thought Processes [Paperback] Daniel Solow (Author)

Hope that helps and gives you some ideas!