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Student[LinearAlgebra]

 MatrixExponential
 determine the matrix exponential

 Calling Sequence MatrixExponential(A, t, options)

Parameters

 A - square Matrix t - (optional) scalar parameter options - (optional) parameters; for a complete list, see LinearAlgebra[MatrixExponential]

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{LinearAlgebra}\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[-13,-10\right],\left[21,16\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{-13}& {-10}\\ {21}& {16}\end{array}\right]$ (1)
 > $\mathrm{MatrixExponential}\left(A\right)$
 $\left[\begin{array}{cc}{15}{}{ⅇ}{-}{14}{}{{ⅇ}}^{{2}}& {-}{10}{}{{ⅇ}}^{{2}}{+}{10}{}{ⅇ}\\ {21}{}{{ⅇ}}^{{2}}{-}{21}{}{ⅇ}& {-}{14}{}{ⅇ}{+}{15}{}{{ⅇ}}^{{2}}\end{array}\right]$ (2)
 > $\mathrm{MatrixExponential}\left(A,x\right)$
 $\left[\begin{array}{cc}{15}{}{{ⅇ}}^{{x}}{-}{14}{}{{ⅇ}}^{{2}{}{x}}& {-}{10}{}{{ⅇ}}^{{2}{}{x}}{+}{10}{}{{ⅇ}}^{{x}}\\ {21}{}{{ⅇ}}^{{2}{}{x}}{-}{21}{}{{ⅇ}}^{{x}}& {-}{14}{}{{ⅇ}}^{{x}}{+}{15}{}{{ⅇ}}^{{2}{}{x}}\end{array}\right]$ (3)
 > $\mathrm{MatrixExponential}\left(A,-x\right)$
 $\left[\begin{array}{cc}{15}{}{{ⅇ}}^{{-}{x}}{-}{14}{}{{ⅇ}}^{{-}{2}{}{x}}& {-}{10}{}{{ⅇ}}^{{-}{2}{}{x}}{+}{10}{}{{ⅇ}}^{{-}{x}}\\ {21}{}{{ⅇ}}^{{-}{2}{}{x}}{-}{21}{}{{ⅇ}}^{{-}{x}}& {-}{14}{}{{ⅇ}}^{{-}{x}}{+}{15}{}{{ⅇ}}^{{-}{2}{}{x}}\end{array}\right]$ (4)

Compatibility

 • The Student[LinearAlgebra][MatrixExponential] command was introduced in Maple 2020.
 • For more information on Maple 2020 changes, see Updates in Maple 2020.

 See Also