\(P\) is called a projection matrix and has 3 rows, 4 columns. This realizes the dimension drop into the projection plane.

The camera is a product which has some properties, most notably it’s a focal length. Important is that these properties are constant for a given camera (assuming you are not zooming). This is the internal set of properties. Then there is an external set of properties which is a position and direction of the camera.

This can be reflected in a matrix language as decomposing the matrix \(P\) into a 3×3 calibration matrix \(K\) (internal matrix with camera properties), and a 3×4 view matrix \(V\) (external matrix with camera position and rotation). These matrices are sometimes called intrinsic and extrinsic. And you drill them down into the following form.