computes the exponential of a matrix

where matrix is any matrix.

Given a matrix , the EXPMATRIX function returns an matrix approximating . The function uses a Padé approximation algorithm as presented in Golub and Van Loan (1989).

Note that this module does not exponentiate each entry of a matrix; for that, use the EXP function.

The following example demonstrates the EXPMATRIX function. For the matrix used in the example, is the matrix Here is the code:

   A = { 1 1, 0 1 };
   t = 3;
   X = ExpMatrix( t*A );
   ExactAnswer = ( exp(t) || t*exp(t) ) //
		 ( 0      ||   exp(t) );
   print X, ExactAnswer;

The output from this code is

            X

   20.085537 60.256611
           0 20.085537

       EXACTANSWER

   20.085537 60.256611
           0 20.085537