Given an 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 element 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 You can compute the exponential matrix as follows:

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