\begin{definition}[Definition:Matrix Exponential]
The '''matrix exponential''', denoted $e^{t \mathbf A}$, of the order $n$ constant square matrix $\mathbf A$, is defined to be the unique solution to the initial value problem:
:$X' = \mathbf A X, \ \map X {\mathbf 0} = \mathbf I$
where:
:$\mathbf I$ is the unit matrix
:$X$ is an order $n$ square matrix which is a function of $t$.
Category:Definitions/Matrix Algebra
\end{definition}