Exercise books in linear algebra and geometry I'm studying Brannan's Geometry and Lang's Introduction to Linear Algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as companions.
The books I'm searching for should be:


*

*full of hard, non-obvious, non-common, and thought-provoking problems;

*rich of complete, step by step, rigorous, and enlightening solutions.

 A: 
A classic in linear algebra is Paul R. Halmos' Linear Algebra Problem Book.
In fact it's also a great book teaching many aspects of linear algebra and a great book in teaching how to solve problems. The first part contains more than 160 problems, the last part contains detailed solutions. A nice idea is a small chapter in between about 15 pages long, which contains hints for each of the problems.

The reader is encouraged even if he is able to solve a problem to also check the solution, since they may contain additional info in form of interesting comments.
I fully agree with the end of his preface:

I hope you will enjoy trying to solve problems.
I hope you will learn something by doing so, and I hope you will have fun.

A: Let me start by mentioning a series of books on linear algebra, by T. S. Blyth and E. F. Robertson, that I consider to be really enlightening:
Theory + Solved Exercises


*

*Basic Linear Algebra

*Further Linear Algebra
Solved Exercises


*

*Algebra Through Practice: Volume 2, Matrices and Vector Spaces

*Algebra Through Practice: Volume 4, Linear Algebra

And now, my secret weapons (more directed towards matrix theory):


*

*Matrix Algebra, by K. Abadir and J. Magnus;

*Problems and Solutions in Introductory and Advanced Matrix Calculus, by Willi-Hans Steeb.


Have fun!
A: I agree with Timbuc, the Schaum's calculus book has helped me with having many solved problems and explanations. I have seen a geometry addition being sold on amazon and ebay for a pretty good price
A: I've studied on this. Actually it's in Italian but it's a wonderful text.
