Module Library

EXPMATRIX Function

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