Eigensolutions sensitivity for nonsymmetric matrices with repeated eigenvalues

1993/07/01 by Angelo Luongo · 7 citations
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Spectral Theory in Mathematical Physics

paper · doi:10.2514/3.11770

Abstract

A perturbation algorithm is developed for evaluating eigenvalue and eigenvector directional derivatives of nonsymmetric defective matrices. Some properties are recalled; in particular, chains of generalized right and left eigenvectors and their orthogonal properties are defined. Small perturbations of the matrix are then considered. An asymptotic expansion of the eigensolutions of the perturbed problem is obtained in terms of noninteger powers of the perturbation parameter. Particular attention is devoted to the eigenvectors of the perturbed system and to the strong coupling that occurs between the chains

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• Sensitivities and Linear Stability Analysis Around a Double-Zero Eigenvalue
• Free vibrations and sensitivity analysis of a defective two degree-of-freedom system
• Linear Stability Analysis of Multiparameter Dynamical Systems via a Numerical-Perturbation Approach
• Higher-Order Eigensensitivity Analysis of a Defective Matrix
• A development of modal expansion method for eigensensitivity analysis of a defective matrix
• Can a semi-simple eigenvalue admit fractional sensitivities?
• Calculation of eigenvalue and eigenvector derivatives of a defective matrix

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