Calculation of camera-monitor relationship matrix

Hi, hope you are having a good weekend.

I installed my webcam and would like to calculate a transformation matrix(Rotation and Transition) from camera coordinate system to monitor coordinate system.

Don't confuse it with camera calibration.

This is a similar example: https://www-users.cse.umn.edu/~stergios/papers/iros08-mirror.pdf.

Deliverable is code written in any language.

Thanks in advance.