Abstract
The tracking of eigenvalues and eigenvectors for parameterized matrices is of major importance in optimization and stability problems. In the present paper, we consider a one-parameter family of matrices with distinct eigenvalues. A complete system of differential equations is developed for both the eigenvalues and the right and left eigenvectors. The computational feasibility of the differential system is demonstrated by means of a numerical example.
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The work of R. Kalaba and L. Tesfatsion was partially supported by the National Science Foundation under Grant No. ENG-77-28432 and by the National Institutes of Health under Grant No. GM-23732-03.
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Kalaba, R., Spingarn, K. & Tesfatsion, L. Variational equations for the eigenvalues and eigenvectors of nonsymmetric matrices. J Optim Theory Appl 33, 1–8 (1981). https://doi.org/10.1007/BF00935172
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DOI: https://doi.org/10.1007/BF00935172