A QR shift is a scalar subtracted before the QR factorization in a QR algorithm step and restored after reversing the factors:The final identity uses the orthogonality of , proving that the eigenvalues are preserved. Choosing a shift near an eigenvalue can accelerate block deflation in the QR algorithm. A common choice is the current bottom-right entry, but it can stall, as in Exact-shift diagonalization of a two-state swap matrix.
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