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Text version of the page
| Powers and Exponentials | |||||||||||||||||||||||||||||||||||||
| computes the matrix exponential. An example is provided by the 3-by-3 coefficient matrix A = | |||||||||||||||||||||||||||||||||||||
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| and the initial condition, x(0) x0 = 1 1 1 The matrix exponential is used to compute the solution, x(t), to the differential equation at 101 points on the interval 0 < t < 1with X= []; for t = 0:.01:1 X = [X expm(t*A)*x0]; end A three-dimensional phase plane plot obtained with plot3(X(1,:),X(2,:),X(3,:),'-o') shows the solution spiraling in towards the origin. This behavior is related to the eigenvalues of the coefficient matrix, which are discussed in the next section. | |||||||||||||||||||||||||||||||||||||
| 1-39 | |||||||||||||||||||||||||||||||||||||