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Variational Equations for the Eigenvalues and Eigenvectors of Nonsymmetric Matrices


  • Kalaba, Robert E.
  • Spingarn, K.
  • Tesfatsion, Leigh S.


This article develops a complete system of ordinary differential equations for tracking the eigenvalues and the right and left eigenvectors of nonsymmetric parameterized matrices over parameter intervals. A simpler reduced form of the ODE system is then derived for tracking the eigenvalues and eigenvectors of symmetric parameterized matrices. The feasibility and accuracy of the tracking method are illustrated by numerical examples. Annotated pointers to related work can be accessed here:

Suggested Citation

  • Kalaba, Robert E. & Spingarn, K. & Tesfatsion, Leigh S., 1981. "Variational Equations for the Eigenvalues and Eigenvectors of Nonsymmetric Matrices," Staff General Research Papers Archive 11219, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:11219

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    Cited by:

    1. Max E. Jerrell, 1999. "Environments for Global Optimization Using Interval Arithmetic and Computational (Automatic) Differentiation," Computing in Economics and Finance 1999 1321, Society for Computational Economics.

    More about this item


    Eigenvalue; eigenvector; ordinary differential equations; nonsymmetric parameterized matrices; solution tracking;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling


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