Somewhat relevant: I've recently taken an algebra course which covered both abstract algebra and linear algebra (those the fields aren't disjoint though), and I've really enjoy this book by Saunders and Birkhoff : Algebra.

It covers abstract algebra in a very thorough, theoretical fashion, with plenty of exercises. It has chapters of Vector Spaces and Matrices, and builds those concepts from the ground up (beginning with the concept of a free module).

I'm studying CS, so obviously this book is miles ahead of the curriculum (the quality of the uni is quite laughable as well, but well) but I set a mental reminder to have another go at this book once I'll have more spare time.