[b]If[/b ] A and B have the same eigenvectors, then the eigenvectors of Carethe sums of corresponding egenvectors of A and B. "Corresponding" here meaning "for the same eigenvector". If and , then (A+B)v= Av+ Bv= \lambda_A v+ \lambda_B v= (\lambda_A+ \lambda_B)v[/tex].

Otherwise, I don't know how you are going to choose which eigenvalues of A and B to add to get eigenvalues of B.