I'm trying to find the general solution for the following 4x4 matrix:
[0 1 1 0]
[-1 0 0 1]
[0 0 0 1]
[0 0 -1 0]
So far, I have the eigenvalues as repeated i, i, - i ,-i
Eigenvector for i: [-i 1 0 0]^t (with multiplicity 2)
Eigenvector for -i: [1 i 0 0]^t (with multiplicity 2)
How do I get the general solution for this? And how do I find the adjoint eigenvectors for a 4x4 with complex repeated eigenvalues?
Of the matrix,
Umm.. I do believe it should look something like x(t) = c_1e^(eigen)(eigenvector) + ... + c_ne^(eigen)(eigenvector)
This is from an ODE's class, but last time I posted a matrix question from ODE's a mod moved it and scolded me. So, that is why I put it in the linear algebra this time.