Combining rotation and translation into one matrix
Rotation matrices describe orientation, but a full pose also needs position, and doing rotation and translation as two separate steps gets clumsy once you start chaining many frames together. The standard fix is the homogeneous transformation matrix, a 4x4 matrix that packages a 3x3 rotation and a translation into a single object. Applying it to a point rotates and shifts that point in one combined operation.
The real payoff shows up when chaining frames. If you know the homogeneous transform from the camera frame to the base frame, and from the base frame to the world frame, you can combine them with a single matrix multiplication to get the direct transform from camera to world. This is exactly the kinematics-arm style chain robotics systems rely on constantly, and it's why homogeneous transforms, not separate rotation-then-translation steps, are the standard tool for multi-frame robotics math.