A virtual camera is easiest to reason about by transforming the scene into a coordinate system attached to the camera.

Suppose the camera has world transform $C$, which places and orients camera coordinates in the world. The view transform is its inverse:

$$V=C^{-1}.$$

Applying $V$ to world-space points makes the camera behave as if it were located at the origin with a standard viewing direction.

This explains an important graphics equivalence: moving the camera one way has the same relative effect as transforming the whole world by the inverse motion.

A camera basis is commonly described by orthogonal right, up and forward directions together with a position. These define the rotation and translation needed for $C$ and therefore for $V$.

Keeping the view transform separate from object transforms lets the same scene geometry be rendered from many viewpoints without modifying the models themselves.