I'm reading a graphics book and this passage is unclear to me (I'm relatively a newbie with linear algebra so I might miss some notions)
Basically the problem here is: I have a transformation and a left-handed coordinate system. This transformation might flip the Z axis thus rendering the left-handed system to a right-handed one. This is bad because we have a vector (the normal vector to a surface) that ends up to be flipped because we calculate it as the cross product between the derivative of the point p we are considering on the surface with respect to the u parametric coordinate of the surface and the derivative of the point p with respect to the v parametric coordinate.
There are some things I don't understand: what does it mean in the formula S(1,1,-1) dp/du ? Is it applying the transformation to the partial derivative or what? And how can I calculate the cross product between two partial derivatives of a point with respect to a coordinate? Is the derivative of a point a vector?
Edit: I figured out that S(1,1,-1) is a simple scale matrix, but I can't understand the passage and where does the S(-1,-1,1) come