Dot Dot Dot

I Gan What?

I'm not sure if I've metioned this before or not, but I'm taking a computer graphics class. Last term, the computer graphics class was more like an introduction to OpenGL and graphics concepts--very fun, but not very technical. This term we are learning how to write our own graphics engine. Very interesting stuff!

I was reading in my execellent textbook, Fundamentals of Computer Graphics by Peter Shirley, when I ran across the chapter on matrix math. Most of the material was giving me linear algebra flashbacks until I hit the section on eigenvalues and eigenvectors. Now it's possible that my linear algebra class covered this, but it's also quite possible I missed it due to sleep deprivation. Either way, I finally understand what eigenvalues are--and they are cool.

Essentially, an eigenvector is a vector that does not change direction when multiplied by a vector, and an eigenvalue is factor the multiplication scales the eigenvector. The reason why this is important is because all tranformations (rotation, scale, translation, shear, etc.) can be represented by matricies. Those matricies are then multiplied by coordinates or vectors to "transform" them to new coordinates or vectors. So, with eigenvalues/vectors, one can determine what will and will not be affected by a particular tranformation. Some matricies, like the rotation matrix, do not have eigenvectors, others like the identity, have infinitely many eigenvectors.

If you are curious and want to know more, check out the eigenvalue entry at MathWorld. Also, if you want a really good textbook on computer graphics with some of the best math summary chapters I have read, then check out the book by Peter Shirley.