A good linear algebra text book?

[nabeel17]

I'm looking for a linear algebra textbook slightly above beginner level to get a good grasp of certain topics. Specifically, I want to understand exactly what the determinant of a matrix is and its relation with volume, linear dependence/independence, etc

I recently figured out how to get the jacobian going from rectangular coordinates to spherical and cylindrical but I don't feel I have an intuitive grasp or understanding of how it works...I can just do the math if that makes sense.

 

[NegativeDept]

I'm a big fan of Mathematical Methods in the Physical Sciences by Mary Boas. It's very popular with most of the theoretical and experimental physics students I know.

This is not a linear algebra book - it's more like several applied math textbooks condensed into short versions and glued together. It includes sections on linear algebra and also a nice visual explanation of the Jacobian determinant of a coordinate transformation. (Don't get discouraged yet! I made a mess of that topic for a long time before I finally developed a decent working intuition. As a bonus, it means you'll get a lot more of the inside jokes in Alice in Wonderland and Through the Looking-Glass.)

One of my favorite study tactics is to go to a library or bookstore, find some textbooks on the subject, and flip through them. Often you can tell pretty quickly whether the style and prerequisites for that book are a good match for your needs.

 

[nabeel17]

Awesome, that's exactly the type of book I need! And I'll take your advice and glimpse through more textbooks at the library.