I found written that if matrix A is real and you use the Power method to find eigenvalues then "If the matrix and starting vector are real then the power method can never give a result with an imaginary part." reference.
Is it also true for the inverse power method used to find a better approximation of the eigenvalue given a initial approximation? I've written a simple MATLAB program and I think it's false but I need some clarification.
What about the initial approximation of complex eigenvalue? Should it be complex in order to converge?