Book recommendation for Linear algebra. I am looking for suggestions, it has to be a self study book and should be able to relate to applications to real world problems.
If it is more computer science oriented , that would be great.

There is an innovative course Coding the Matrix offered by Philip Klein which consists of a book and a course offered on Coursera and other places. It even has a Twitter account for keeping updated. The reviews are controversial, see also here and here, but it looks as an interesting challenge to try. It is designed, according to the author's website, as a "course is to provide students interested in computer science an introduction to vectors and matrices and their use in CS applications".
