1993/07/01 by Angelo Luongo · 43 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Defective matrix #Diagonalizable matrix #Eigenvalue perturbation #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Modal matrix #Perturbation (astronomy) #Physics #Spectral Theory in Mathematical Physics #Symmetric matrix
paper · doi:10.2514/3.11770
published in AIAA Journal 31(7), 1321-1328 (American Institute of Aeronautics and Astronautics)
openalex publication_date 1993/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
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