I've seen a few other posts on this topic but none have full answers.
I'm trying to implement some eigen-decomposition algorithms. I've managed to get the Explicit QR algorithm and the Implicit (Francis) algorithm to compute the eigenvalues. My question however relates to computing the eigenvectors.
My core question is:
Do I need to use the Inverse Iteration Algorithm to get the eigenvectors after completing the QR algorithm?
I understand additionally that I'll need to use the transformation matrices from my QR algorithm (balancing, the hessenberg reduction and the QR decomposition). But I'm more interested right now in whether there is some way to get the eigenvectors from the QR algorithm itself (as wikipedia implies there is).