mpower - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

MTM

 mpower
 matrix power

 Calling Sequence mpower(A,x) mpower(x,A)

Parameters

 A - square matrix or array x - scalar

Description

 • The mpower(A,x) command returns the matrix power ${A}^{x}$.
 • The mpower(x,A) command returns the power ${x}^{A}$.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2\right],\left[3,4\right]\right]\right):$
 > $x≔3:$
 > $\mathrm{mpower}\left(A,x\right)$
 $\left[\begin{array}{cc}{37}& {54}\\ {81}& {118}\end{array}\right]$ (1)
 > $B≔\mathrm{Matrix}\left(\left[\left[1,2\right],\left[2,1\right]\right]\right):$
 > $x≔3:$
 > $\mathrm{mpower}\left(x,B\right)$
 $\left[\begin{array}{cc}\frac{{41}}{{3}}& \frac{{40}}{{3}}\\ \frac{{40}}{{3}}& \frac{{41}}{{3}}\end{array}\right]$ (2)

This is the same as:

 > $\mathrm{LinearAlgebra}:-\mathrm{MatrixExponential}\left(\mathrm{ln}\left(x\right)B\right)$
 $\left[\begin{array}{cc}\frac{{41}}{{3}}& \frac{{40}}{{3}}\\ \frac{{40}}{{3}}& \frac{{41}}{{3}}\end{array}\right]$ (3)