Matrix transforms; concepts and theory, are there

Question

I've been having fun rendering charts and graphs from co-ordinates lately, and I'm fascinated by using matrices to transform co-ordinate spaces.

I've been able to successfully scale and invert 2 dimensional co-ordinate spaces, but now my appetite is whetted. :)

Where can I go for clear, informative, (free), educational material on matrices, matrix math, especially as applies to 2 and 3 dimensional space?

Answer 1

MIT has alot of their math courses' materials online at http://ocw.mit.edu/OcwWeb/Mathematics/. Once you have the basics down, they have the physics notes online too.

Answer 2

One of the best books for beginners is Carl Meyer's "Matrix Analysis and Applied Linear Algebra".

You can view the entire book online here (although it has a copyright watermark): http://www.matrixanalysis.com/DownloadChapters.html

You might want to take a look at Chapter 5 pg. 326 - 332 which covers the rotations in 3 dimensional computer graphics

Answer 3

MIT-OCW's course on Linear Algebra by Gilbert Strang. Incredible lectures by an incredible man; if your understanding of matrices is solely derived from programming sources (like MATLAB) then a course on Linear Algebra will definitely give you the fundamentals to do crazy things with matrices.

http://www.ocw.cn/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm

Answer 4

Those are the information that I found. Some of them might be valuable to You:

Theory:

• Woflrams Information about matrices and additional ones on Wikipedia
• Matrices by Pam Norton - very good book, available at Google Books for free.
• Orthographic and perspective projections
• 3D transformations at MSDN

(Searching for "Matrices" at Google books gives You lots of lecutures, some of which are directly connected with transformations - this is one of the first results, but I cheer You to check more.)

• Articles like this one, or maybe this or this are easily found with help of Google, so I will not post more.
• There were also few questions about matrices on StackOverflow.com : Using 3d transformation matrices and How to apply a transformation matrix? are just first few examples, You can find more looking for the matrix or math tags.

I also encourage (I don't know if this is the right word, I am just learning English) You, to look for this kind of information in one of those books (though they are not free, but You can find large parts of older ones on Google Books):

1. Game programming gems 7
2. Game programming gems 6
3. Game programming gems 5
4. Game programming gems 4
5. Game programming gems 3
6. Game programming gems 2
7. Game programming gems

Each of those has section about math gems - and there are lots of neat tricks there. Those books are worth every cent.

There are also GPU Programming gems, so You might try them too.

Practice:

• OpenGl Book at Wikipedia has section about matrices in OpenGl (also, using matrices in OpenGl is described here and here)
• Drawing 3D room in DirectX + info about matrix transformations.

If I will find more, I will edit and add links here, but to be honest - I found those links in about 10 minutes of using google. World's most popular browser stores data about everything - and yes, "everything" means matrices too.

Cheers, Mate.