Why does camera matrix change on Rectification or change of resolution ?

edit

Hi,

Recently I've been working with rectified /undistorted images (from a single camera) and I had to use the "P" matrix from the output of the ROS monocular calibration process (and things work fine). But can someone explain -

1. Why does the camera matrix change due to rectification/undistortion process ?

2. I also noticed the camera matrix had to be scaled accordingly when switching resolutions of my camera. Again, why is this the case ? ( I understand that the principal point (cx,cy) will change but the focal length also changes. I would have thought focal length is something physical and can only be changed with an optical zoom or something similar ..)

Thanks!