Module Library |

**computes the exponential of a matrix**

**EXPMATRIX(***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, p. 558).

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

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