## eigenvalues and eigenvectors (Rayleigh quotient method)

Let A be a 3X3 real symmetric matrix. Let the eigenvalues of A be r1, r2 and r3, and the corresponding unit eigenvectors be q1, q2 and q3. We assume that r1 not equal to rj for j =2, 3. Futhermore, we can assume that the eigenvectors are orthogonal to each other. Let x0 be a vector that is close to q1:

x0 = q1 +e2q2 +e3q3,

where e1, e2 are small constants. Calculate x1 be one step of the Rayleigh quotient method.