Why is the "matrix from standard camera to world space" defined as it is in this slide?
I would've expected this matrix to be the exact opposite (ie: the "matrix from world space to camera space") because we defined the coordinate system transform as a matrix of basically [u,v,o] where u,v are basis vectors and o is the origin. Given that, it seems like all we need to do is plug in the camera's equivalent u,v,o vectors to get the "Look-at" transformation.
It's possible I have a misunderstanding of what the "look-at" transform is supposed to be, but I just expected it to be a simple coordinate transform and this slide seems to suggest otherwise.
@lakerpaxtan I may be wrong, but my understanding is that we are shifting our coordinate system, not transforming an object to a new coordinate system. https://cs184.eecs.berkeley.edu/sp20/lecture/4-41/transforms captures this. A coordinate-shifting transform is the inverse of the equivalent direct transform of an object within the space.
@Aidan brings up a very fundamental property of coordinate transforms in general. In physics, this duality is represented by covariant vs contra-variant transformations, and is a much, much deeper topic than needs to be considered here, but Wikipedia and other videos can be good starting points to learning about them!