Source: /cirosantilli/matrix-exponential

= Matrix exponential

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>.

{title=How (and why) to raise e to the power of a matrix by <3Blue1Brown> (2021)}