My goal is to understand how to use a transformation matrix in tandem with transform_world() to be able to make transformations to my PF_EffectWorld. In particular I wasn't sure if each index of the matrix represents a certain transformation property, or how it works. I can already move my image using arbitrary values in the configuration above, but doing things like rotation seem to be a bit more complex.
@shachar carmi Another question along the lines of how to say rotate using this method, is the matrix applied based on the current transformation setup of an EffectWorld, and it sort of moves it accordingly?
there is no "current transformation" to a Transform world. it transforms the imput image according to the supplied matrix, and the result is transformed along with the layer.
rotating an image using a 3X3 matrix involves placing sin and cos (and negative values) in certain places in the matrix. this is common practice in 2D and 3D graphics, and you can find literally hundreds of tutorials and code samples in a google search. the AE transformation matrix is no different from what you'll find in these tutorials and code samples, with the exceptsion that it's lines and rows are swapped to what is generally used.
the wikipedia link i sent would be good starting point to find what to look for in your serached.
3X3 matrices can translate, rotate, scale and skew an image, all in one concatenated matrix. actually, the standard AE effect "transform" does just that.