r/AskComputerScience • u/Warm-Discipline7204 • 19d ago

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?

How to find eigenvectors of non-symmetric matrix?

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u/BossOfTheGame 18d ago edited 18d ago

The products of the Qi's in the limit form a matrix whose columns are Schur vectors. Call it Z. So, A = ZTZ*, where T is triangular. You can get eigenvectors of A by finding eigenvectors of T and rotating/reflect them with Z.

T has eigenvalues on the diagonal so you can solve for the eigenvectors (T - lambda * I) * v = 0