Exponentiating $2\times 2$ and $3\times 3$ Matrices Done Right

Angel P. Popov, Todor D. Todorov

We derive explicit formulas for calculating $e^A$, $\cosh A$, $\sinh A,\cos A$ and $\sin A$ for a given $2\times 2$ matrix $A$. We also derive explicit formulas for $e^A$ for a…