(c) The QR iteration with shifts for computing the eigenvalues of a matrix A € R™×n takes the form 1 Ho = U" AU (initial reduction to upper Hessenberg form) 2 for k = 1, 2, . .. H – HRI =:QµRp (QR factorization, µk possibly complex) H41:= RµQk + HkI 3 4 5 end (i) Show that each iteration represents a similarity transformation. (ii) Define an upper Hessenberg matrix and explain why we begin by reducing A to upper Hessenberg form.

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Q: Pls show me step by step

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