I’m working on a program using Wolfram Mathematica that can give us the exponential matrix as a result. I have a 3x3 system as a base (but it may work with a nxn one), which gives me 3 linear equations that involve alphas and lambdas with their respective “t’s”. So far, I don’t know how to turn that system into a matrix to get this form: e^( λi) = A α* . I would like to know if there is a way where I can take those α’s away from my equations (attached image) and put them into an independent vector, so I can proceed to to this: α = A^-1 * e^( λi); “A” would be the matrix formed from the Eigenvalues and alphas polynomial equation showed below.
I would appreciate if you could help me with this situation.
Greetings!
P.S. I’m not allowed to use any shortcut like Solve or Matrix Exp.
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int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]
I am afraid I don’t understand your problem. What do you think about this?
mm = Partition[RandomReal[{0, 10}, 9], 3];
mm // MatrixForm
ev = Transpose[Eigenvectors[mm]];
ev // MatrixForm
dia = Inverse[ev].mm.ev // Chop;
dia // MatrixForm
expm = Exp[dia t];
expm // MatrixForm
result = FullSimplify[ev.expm.Inverse[ev]];
result // MatrixForm
