Exercise books in linear algebra and geometry

Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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

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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!

Answer 4

I've studied on this. Actually it's in Italian but it's a wonderful text.