$2.$ To accelerate the convergence of QR algorithm, we can also consider a shifted version of QR algorithmChoose A$(0)=($Q$(0))$T AQ$(0)$ with orthogonal Q$(0)$ Rn$\backslash$times nfor k $=1,2,...,$Choose a shift $$kCompute QR decompostion A$($k$1)$kI $=$ Q$($k$)$R$($k$)$A$($k$)=$ R$($k$)$Q$($k$)+$kIendWith a proper choice of $$k$,$ the above algorithm will converge super fast. Prove that A$($k$)$ is similarto A

To accelerate the convergence of $QR$ algorithm, we can also consider a shifted version of $QR$ algorithmWith a proper choice of mu$\_($k$),$ the above algorithm will converge super fast. Prove that A$^(($k$))$ is similar to A$.$