The matrix exponential A is defined by the McLaurin series This computation can be quite difficult, as this problem illustrates.  Enter the function  Apply matexp to the matrix to obtain the matrix...

The matrix exponential

^A
is defined by the McLaurin series

This computation can be quite difficult, as this problem illustrates.

 Enter the function

 Apply matexp to the matrix

to obtain the matrix A_McLaurin.

 A_McLaurin is far from the correct result. Compute the true value of

^A
using the MATLAB function expm as follows:

>> A_true = expm(A);

The function uses the Padé approximation [21].

 Explain why the result in part
 is so far from the correct result. Use MATLAB help by typing

Remark 8.8. The text by Laub [22, pp. 6-7] has a very interesting example dealing with the matrix exponential.