Eigensensitivity Analysis of a Defective Matrix

摘要

The formulas for calculating the first-to third-order perturbation coefficients of the eigenvalues and the first order perturbation coefficients of eigenvectors of a defective matrix are derived by use of the direct perturbation method for the case where the eigenvalue problem for the first-order perturbation coefficients of the eigenvalues of the defective matrix has repeated eigenvalues. Associated with νth-order Jordan blocks of the matrix, the perturbation equations are derived by expanding the perturbed eigenvalues and eigenvectors in power series of η=ε_1/v, where εis the small parameter of the problem, substituting the series into the perturbed eigenvalue problem and comparing the power of η.