1 real and 2 complex eigenvalues, Programming Languages

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1 Real and 2 Complex Eigenvalues   

From the real eigenvalue/vector pair, l1 and ?h1

el1t ?h1

We find the other two solutions in identical manner which we did with the 2x2 case.  If the eigenvalues are l2,3 = a + bI with eigenvectors ?h2 and ?h3   We can find two real-valued solutions through using Euler's formula to expand;

el2t ?h2 = e(a + bi)t ?h2   = eat (cos(bt) + i sin(bt))  ?h2

in its real and imaginary parts, u? + i v? .  The final two real valued solutions we need are then,

u?                                           v?


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