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Is it true that in general the general $QR$ algorithm applied to $A$, a multiple shift of degree $r$ is equivalent to a sequence of $r$ single shifts of degree $1$? (Assuming that no shift is an exact eigenvalue of $A$). (Equivalent in the sense that the computed matrices equivalent in the sense that the computed matrices $A_k$ coincide up to diagonal, unitary simliarity transformations. How can I show that?

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