Definition:Matrix Exponential

Definition
The matrix exponential, denoted $e^{\mathbf A t}$ for the 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 identity matrix.