[riperoni]

This is a nice writeup, but the definition and usage of determinant makes my nails curl.

A determinant is defined for matrices, not for vectors and from the purpse of your article I think you skipped over that part for simplicty/brevity. But really, introducing it once properly, then going to the more pragmatic definition of yours aknowledging that it is skipping some parts would be so much better for someone not knowing this field in depth. Or just not calling it determinant. And mentioning that determinants show a sort of scale factor of transformation, also for 3D, would be nice to connect to 3D rendering and such.

Since it is meant as intro/tutorial on implementation I would really point into all the right math-relates directions as a reference. Whoever wants, can read or skip those parts.