Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Abstract

In many engineering applications, the physical quantities that have to be computedare obtained by solving a related eigenvalue problem. The matrix under consideration and thusits eigenvalues usually depend on some parameters. A natural question then is how sensitive thephysical quantity is with respect to (some of) these parameters, i.e., how it behaves for small changesin the parameters. To find this sensitivity, eigenvalue and/or eigenvector derivatives with respect tothose parameters need to be found. A method is provided to compute first order derivatives of theeigenvalues and eigenvectors for a general complex-valued, non-defective matrix.