I'm looking for a name for my class that manipulates 4x4 matrices that handle position, rotation, and scale. Is there a common word that encompasses all three?
(I'm splitting the matrix math into its own file/class.)
transform, or transformation
If you add shear to your list (although rarely used in games), it is generally known in mathematics as an affine transformation.
The general term 'transformation' has been mentioned already, is a usually considered a superset and includes projection transformations as well (which are not affine).