Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – Application of perturbation theory for simple invariant subspaces

Perturbation bounds for the relative error in the eigenvalues of diagonalizable and singular matrices are derived by using perturbation theory for simple invariant subspaces of a matrix and the group inverse of a matrix. These upper bounds are supplements to the related perturbation bounds for the eigenvalues of diagonalizable and nonsingular matrices.