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

e^l1^t ?h₁

We find the other two solutions in identical manner which we did with the 2x2 case. If the eigenvalues are l_2,3 = a + bI with eigenvectors ?h₂ and ?h₃ We can find two real-valued solutions through using Euler's formula to expand;

e^l2^t ?h₂= e⁽^{a + b}ⁱ⁾^t ?h₂ = e^a^t (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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