When do we get complex eigenvalues?... | Filo

SOLVED: 5.2.2 (Complex eigenvalues) This exercise leads you through the solution of a linear system where the eigenvalues are complex. The system is X - fexty. a) Find A and show that it has eigenvalues Ap = 1 i, Aq = 1 - i, with eigenvectors v1 = (i, 1), v2 = (-i, 1). (Note that the eigenvalues are complex conjugates; and so are the eigenvectors. This is always the case for real A with complex eigenvalues.) b) The general solution is x(t) = e^(v1t) e^(v2t). So in one sense we're done.

Complex Eigenvalues: Example | Differential Equations | Mathematics | MIT OpenCourseWare