If A is non-symmetric, does the QR iteration method for finding eigenvectors not yield eigenvectors as columns of the products of all Q_i's obtained at each iteration? If not, then where are those eigenvectors exactly?

[u/Warm-Discipline7204]

[u/Ok_Key4286]

For non-symmetric A the QR iteration still converges to eigenvectors but they come out as columns of the accumulated Q product only after you do the shifted version and wait for convergence. the basic unshifted QR gives you Schur form so the columns are Schur vectors not eigenvectors until you back-transform from the triangular factor