Definition:Matrix Exponential

Definition
The matrix exponential, denoted $e^{t \mathbf A}$, of the $n \times n$ constant matrix $\mathbf A$, is defined to be the unique solution to the initial value problem:
 * $X' = \mathbf A X, \ X \left({\mathbf 0}\right) = \mathbf I$

where $\mathbf I$ is the unit matrix, and $X$ is an $n \times n$ matrix which is a function of $t$.