Check out this classic from 3b1b - How (and why) to raise e to the power of a matrix: https://youtu.be/O85OWBJ2ayo
https://sassafras13.github.io/MatrixExps/
“Thanks to a fabulous video by 3Blue1Brown [1], I am going to present some of the basic concepts behind matrix exponentials and why they are useful in robotics when we are writing down the kinematics and dynamics of a robot.”