The MatrixExponential(A, t) command returns the Matrix exp(A*t) = I + A*t + 1/2!*A^2*t^2 + ... where I is the identity Matrix.

If the scalar parameter t is not specified, the first indeterminate (if any) in the Matrix is removed and used as a parameter.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{LinearAlgebra}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[-13\,-10\right]\,\left[21\,16\right]\right]\right)$

$A≔\left[\begin{array}{cc}\mathrm{-13}& \mathrm{-10}\\ 21& 16\end{array}\right]$

$\mathrm{MatrixExponential}\left(A\right)$

$\left[\begin{array}{cc}15\ⅇ-14{\ⅇ}^2& -10{\ⅇ}^2+10\ⅇ\\ 21{\ⅇ}^2-21\ⅇ& -14\ⅇ+15{\ⅇ}^2\end{array}\right]$

$\mathrm{MatrixExponential}\left(A\,x\right)$

$\left[\begin{array}{cc}15{\ⅇ}^x-14{\ⅇ}^{2x}& -10{\ⅇ}^{2x}+10{\ⅇ}^x\\ 21{\ⅇ}^{2x}-21{\ⅇ}^x& -14{\ⅇ}^x+15{\ⅇ}^{2x}\end{array}\right]$

$\mathrm{MatrixExponential}\left(A\,-x\right)$

$\left[\begin{array}{cc}15{\ⅇ}^{-x}-14{\ⅇ}^{-2x}& -10{\ⅇ}^{-2x}+10{\ⅇ}^{-x}\\ 21{\ⅇ}^{-2x}-21{\ⅇ}^{-x}& -14{\ⅇ}^{-x}+15{\ⅇ}^{-2x}\end{array}\right]$

The Student[LinearAlgebra][MatrixExponential] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.