As I was working on porting the rotation matrices for the helios.math.transform library, I took a detour to formalize the underlying linear algebra. My goal was to move beyond treating the rotational part of the model matrix as just a black box and instead understand it from a coordinate system perspective.

This led me to writing an article that derives the model matrix as a change-of-coordinates transformation and proves the equivalence between pre-rotating the matrix and post-rotating the transformed vector. If you’re interested in the mathematical foundations of these essential transformations, you can read the full derivation here.