matrix exponential?



On 15/10/06, Ron Crummett <rcrummett at uidaho.edu> wrote:
> Is there a special function to calculate the exponential of a matrix?

Sort of. Try user-contribbed, (the admittedly very
unintuitively-named) "diag" package:

(%i1) load("diag");
(%o1)           /usr/share/maxima/5.9.3/share/contrib/diag.mac
(%i2) A : matrix([2,1],[0,2]);
                                   [ 2  1 ]
(%o2)                              [      ]
                                   [ 0  2 ]
(%i3) mat_function(exp,A);
                                 [   2    2 ]
                                 [ %e   %e  ]
(%o3)                            [          ]
                                 [        2 ]
                                 [  0   %e  ]

You can also use any other analytic function instead of "exp", thanks
to a theorem of functional analysis that if all the eigenvalues of a
matrix A lie within an open set on which f is analytic, then f(A)
makes sense. In case you ever wanted to know what a cosine of a matrix
is, for example. ;-)

HTH,
- Jordi G. H.