"The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function."

Where $X$ is a real or complex square matrix, $e^X \equiv \sum\limits_{k=0}^\infty \cfrac{X^k}{k!}$. $X^0$ is defined to be the identity matrix with the same dimensions as $X$. This is analogous to $e^x = \sum\limits_{k=0}^\infty \cfrac{x^k}{k!}$, where $x$ is a real or complex number.