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:
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.
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
And now, my secret weapons (more directed towards matrix theory):
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
I’ve studied on this. Actually it’s in Italian but it’s a wonderful text.