On condition numbers of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil

摘要

This paper considers the condition numbers of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil. Based on the directional derivatives of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil analytically dependent on several parameters, different condition numbers of a nondefective multiple eigenvalue are introduced. The computable expressions and bounds of introduced condition numbers are derived. Moreover, some results on the perturbation of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil are given.