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Nonsingular M-matrices: a Tour in the Various Characterizations and in Some Related Classes

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  • Giorgio Giorgi

    (University of Pavia)

Abstract

The main purpose of the present paper is to give a unified account of the various characterizations of nonsingular M-matrices and a unified "path" the mathematical proofs concerning the equivalences of the said characterizations. Some related classes of matrices are investigated and some economic applications are discussed

Suggested Citation

  • 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.
    • Handle: RePEc:pav:demwpp:demwp0206
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0206.pdf
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    References listed on IDEAS

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    1. Pearce, Ivor F., 1974. "Matrices with dominating diagonal blocks," Journal of Economic Theory, Elsevier, vol. 9(2), pages 159-170, October.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, January.
    3. Okuguchi, Koji, 1978. "Matrices with dominant diagonal blocks and economic theory," Journal of Mathematical Economics, Elsevier, vol. 5(1), pages 43-52, March.
    4. Giorgio Giorgi & Cesare Zuccotti, 2014. "Some Extensions of the class of K-matrices: A Survey and Some Economic Applications," DEM Working Papers Series 075, University of Pavia, Department of Economics and Management.
    5. Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
    6. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676, November.
    7. 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.
    8. Peris, Josep E & Villar, Antonio, 1993. "Linear Joint-Production Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 735-742, October.
    9. Giorgio Giorgi & Cesare Zuccotti, 2015. "An Overview on D-stable Matrices," DEM Working Papers Series 097, University of Pavia, Department of Economics and Management.
    10. Fuad Aleskerov & Hasan Ersel & Dmitri Piontkovski, 2011. "Linear Algebra for Economists," Springer Texts in Business and Economics, Springer, number 978-3-642-20570-5, July.
    11. 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.
    12. De Giuli, M.E., Magnani, U. & Moglia, P., 1994. "Some remarks on matrices with dominant diagonal," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 5(2), pages 141-151.
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    Cited by:

    1. Giorgio Giorgi, 2024. "A Proof of a Gantmacher’s Result on Nonnegative Square Matrices by Means of M-matrices," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 16(1), pages 1-46, December.

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    Keywords

    M-matrices; K-matrices; Z-matrices; Leontief input-output models; linear economic models;
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