On the sensitivity of multiple eigenvalues of nonsymmetric matrix pencils

This paper considers the sensitivity of semisimple multiple eigenvalues and corresponding generalized eigenvector matrices of a nonsymmetric matrix pencil analytically dependent on several parameters. The directional derivatives of the multiple eigenvalues are obtained, and the average of eigenvalues and corresponding generalized eigenvector matrices are proved to be analytic. The results can be used to define the sensitivity of the semisimple multiple eigenvalues and corresponding generalized eigenvector matrices. These are useful for investigating structural optimal design, model updating, and structural damage detection.