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An Overview on D-stable Matrices

Author

Listed:
  • Giorgio Giorgi

    (Department of Economics and Management, University of Pavia)

  • Cesare Zuccotti

    (Department of Economics and Management, University of Pavia)

Abstract

We give an overview on the main properties of D-stable matrices, i.e. of those square matrices $A$ for which the product DA is stable for any choice of the diagonal matrix D, with all positive diagonal elements. These matrices, introduced in economic analysis by Arrow and Mc Manus (1958), have found, besides applications in mathematical economics, applications also in other fields, such as mathematical ecology, population dynamics, the theory of electric circuits, analysis of neural networks, control theory and other questions.

Suggested Citation

  • Giorgio Giorgi & Cesare Zuccotti, 2015. "An Overview on D-stable Matrices," DEM Working Papers Series 097, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0097
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0097.pdf
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    References listed on IDEAS

    as
    1. Beavis,Brian & Dobbs,Ian, 1990. "Optimisation and Stability Theory for Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521336055, January.
    2. Johnson, Charles R., 1975. "A characterization of the nonlinearity of d-stability," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 87-91, March.
    3. Khalil, Hassan K., 1980. "A new test for D-stability," Journal of Economic Theory, Elsevier, vol. 23(1), pages 120-122, August.
    4. P. K. Newman, 1959. "Some Notes on Stability Conditions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(1), pages 1-9.
    5. James Quirk & Richard Ruppert, 1965. "Qualitative Economics and the Stability of Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(4), pages 311-326.
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    Cited by:

    1. Giorgio Giorgi, 2022. "Nonsingular M-matrices: a Tour in the Various Characterizations and in Some Related Classes," DEM Working Papers Series 206, University of Pavia, Department of Economics and Management.
    2. Pandey, Ayush & Lehe, Lewis J., 2024. "Congestive mode-switching and economies of scale on a bus route," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).

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    Keywords

    D-stability of matrices; stability of matrices.;

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