I am trying to apply the Rayleigh quotient iteration to the matrix A= a 0 0 b where a is different from b (a and b are reals). Find the subsets S of R^2(Reals^2) having the property that the iteration applied to this matrix with initial guesses in S do not converge. Is S a set of measure 0? I know the Rayleigh quotient is R(A,x)=x*Ax/x*x for A Hermitian and x nonzero. I am supposed to begin with an eigenvalue guess mo and an eigenvector guess vo and use the R.Q. but I am not sure which guesses should I begin with. I am not sure how to proceed here. Any help is much appreciated.