Structured Condition Numbers of Multiple Eigenvalues
María José Tirado Peláez, Julio Moro · PAMM · 2006
Abstract We analyze the influence of matrix structure on the condition number of multiple, possibly defective eigenvalues. We show that the structured and unstructured Hölder condition numbers coincide for multiple eigenvalues of matrices belonging to certain classes of structured matrices, which can be characterized as either Jordan or Lie Algebras. We do this by explicitly finding a specific perturbation matrix, analogous to the classical Wilkinson perturbation, which attains the maximal variation within the class of structured matrices. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)