The verification of multiplicity support of a defective eigenvalue of a real matrix

摘要

Computing a defective eigenvalue is an ill-posed problem if components of the matrix are approximate data. Using the definition of multiplicity support of a defective eigenvalue introduced by Zeng, we consider the verification about the sensitivity and computation of a defective eigenvalue of a real matrix. We discuss how to construct a slightly perturbed interval matrix which is guaranteed to possess a real matrix with computed defective eigenvalue of computed multiplicity support. Furthermore, we also obtain an interval matrix which is guaranteed to possess a real matrix. The columns of the real matrix span the corresponding eigenvector space.