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For a nonzero real vector $x$, the Rayleigh quotient of the matrix $A$ isThe Rayleigh quotient iteration starts from a unit vector $v_0$. Given $v_k$, compute the shiftsolve the linear systemand normalize in the Euclidean norm:The next eigenvalue estimate is ${\mu }_{k+1}=R_A(v_{k+1})$. The process stops when the eigenpair residual is sufficiently small.