= Matrix exponential
{wiki}
Is the solution to a <system of linear ordinary differential equations>, the <exponential function> is just a 1-dimensional subcase.
Note that more generally, the <matrix exponential> can be defined on any <ring (mathematics)>.
The matrix exponential is of particular interest in the study of <Lie groups>, because in the case of the <Lie algebra of a matrix Lie group>, it provides the correct <exponential map>.
\Video[https://www.youtube.com/watch?v=O85OWBJ2ayo]
{title=How (and why) to raise e to the power of a matrix by <3Blue1Brown> (2021)}