Question: Let Ak = QkRk. k= 1,2,... be the sequence of matrices derived from A = A1 by applying the QR algorithm. For each positive integer

Let Ak = QkRk. k= 1,2,... be the sequence of matrices derived from A = A1 by applying the QR algorithm. For each positive integer k, define
Pk = Q1Q2 . . . .Qk and Uk = Rk . . . .R2R1
Show that
PkAk+1 = APk
For all k ≥ 1.

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