Quote Originally Posted by chronozphere
I may be wrong, but I think when the scaling is non uniform e. g. (1,2,3)
then the scaled base vectors will not be orthogonal anymore.
Do you mean that the basevectors are not perpendicular anymore??
Yeah.. that can happen. It'll change the area between (0.0.0) and (1.1.1) into a parallelogram.
I think it will happen when you create a rotation matrix and scale it afterwards. But i dont think it's a problem... those are still valid basevectors. isn't it :?
Yes they are (I was wrong in my first post). Base vectors must be linearly independent and don't have to be orthogonal (perpendicular) to each other.

But if they are non orthogonal, then they don't describe cartessian coordinate system, so they are rather useless.