You should look for a book titled "Linear Algebra", look for a low level undergraduate text, or if you are in college, take a linear algebra class, you will learn mostly all you need about matrices for 3D programming.

You know, I do not like all those generic cookie-cutter books.

Off the top of my head, the only book recommendation I have for you is a single chapter in Game Programming Gems 7. Charles River has failed to publish the Table of Contents despite my personal direct request, and although I myself was section editor and edited this chapter last year, I don't recall the exact name of the chapter. It is something along the lines of extracting collision-detection metrics from transformation matrices. I believe it to be useful, and to do a good job of making transformation matrices fairly intuitive.

I also would recommend that you look through the GDC presentations available at Jim van Verth's Essential Math website. These are fairly lightweight (though occasionally deep) presentations that discuss game physics and collision detection. This is really an excellent introductory course, and I believe it may answer some of your questions about transformation matrices. See the sticky thread in this forum on physics engines for a link to that site.

The one thing I can think of that is probably missing from the above is a basic tutorial on 3D projections in general. That is, the book chapter talks about metrics, but doesn't really talk about how a transformation matrix represents a projection from one coordinate frame into another. I unfortunately don't have a good reference handy that I can specifically recommend to do a good job at explanning projections. The "Essential Math..." book by Jim van Verth and Lars Bishop (2nd edition newly published) might suffice....my copy is at home so I can't quickly review and make a specific recommendation. Similarly, there is a book called "Geometric Tools for Computer Graphics" that talks about projections, though it's math heavy and if you use that book I would visit Dave Eberly's Geometric Tools website to find several corrections and advise about using the book.

Hope that helps!

[Edited by - grhodes_at_work on June 9, 2008 10:35:49 AM]

There's a long sample chapter here that introduces vectors, and an excellent sample chapter here that introduces matrices, and both do so in the context of graphics and game programming.