Given a Matrix $A\in\mathbb{C}^{n\times n}$. I want to consider different (for now isolated) cases of eigenvalues/eigenvectors and would like to know what the QR-algorithm produces. Denote $E_{\lambda_i}$ the eigenspace corresponding to $\lambda_i$, $\alpha$ its algebraic multilicity and $\gamma:=\dim E_{\lambda_i}$ its geometric multiplicity.
Case 1: The matrix has dominant eigenvalue $\lambda_1$ and $\gamma = \alpha$. This means the eigenvalue is non-degenerate.
Case 2: The matrix has dominant eigenvalue $\lambda_1$ and $\gamma < \alpha$. This means the eigenvalue is degenerate.
Case 3: The matrix has dominant eigenvalue $\lambda_1$ and there exists another eigenvalue $\lambda_2$ for which $\lambda_1\ne \lambda_2$ but $|\lambda_1|= |\lambda_2|$ and $\gamma = \alpha$ for both eigenvalues.
How does the block Schur-form produced by the QR algorithm in this case look?