I was trying to find the rotation matrix between two camera systems for epipolar geometry when I have the rotation matrices for each camera plane from a common coordinate system. I came upon this question where the accepted answer says to take the inverse of one and multiply with the other, I am wondering why that is?
With 2 generic rotational matrices referenced to the world coordinates you have:
R01 is the rotation from reference system 1 (first camera) to system 0 (world)
R02 is from system 2 (second camera) to system 0
It is also true that the inverse inv(R02) is equal to R20 (from world to second camera system)
So (read every operation right to left)
inv(R02)*R01 =
= R20*R01 =
= R21
You transform coordinates in system 1 to system 2 trough system 0 (I'm not considering relative translation now)