What is the state vector of the system after measuring a degenerate eigenvalue? Surely there are infinitely many vectors of norm 1 that it could be since the degenerate eigenvector span a 2d subspace. Say that we e.g. have a system where the operators eigenvalues are degenerate such that: (1,0), (0,1) both represent eigenvectors of same eigenvalue. How can we ever know what state the particle is in after measurement?