what is r again? It should be whatever the x axis basis vector gets transformed to, right?

Sorry, $\mathbf{r}$ is accidentally not defined here! It is the vector pointing to the right from the perspective of the photographer.

thanks!

And yes, @no4jargon, you are right that the $x$ axis (conceptually in camera space) gets mapped on to the $\mathbf{r}$ vector (conceptually in world space).

But we need to be careful about which transform performs that described mapping. Is it the Look At transform? No! It’s the inverse of that transform. Why?

And why do you think the “Look At” transform is defined in this direction and given that name?