Invariant subspace perturbations related to defective eigenvalues of $\mathrm{\Delta }$-Hermitian and Hamiltonian matrices

Structured perturbation results for invariant subspaces of $\mathrm{\Delta }$-Hermitian and Hamiltonian matrices are provided. The invariant subspaces under consideration are associated with the eigenvalues perturbed from a single defective eigenvalue. The results show how the original eigenvectors and generalized eigenvectors are involved in composing such perturbed invariant subspaces and eigenvectors.