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Eigenvalues with the QR algorithm and Lanczos' method

Suppose ˆA is the triangular matrix we obtained after the Householder transformation, ˆA=ˆQˆU, and multiply from the left with ˆQ1 resulting in ˆQ1ˆA=ˆU. Suppose that ˆQ consists of a series of planar Jacobi like rotations acting on sub blocks of ˆA so that all elements below the diagonal are zeroed out ˆQ=ˆR12ˆR23ˆRn1,n.