IDEAS home Printed from https://ideas.repec.org/p/pav/demwpp/demwp0206.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0206.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
    2. Pearce, Ivor F., 1974. "Matrices with dominating diagonal blocks," Journal of Economic Theory, Elsevier, vol. 9(2), pages 159-170, October.
    3. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    4. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676.
    5. Okuguchi, Koji, 1978. "Matrices with dominant diagonal blocks and economic theory," Journal of Mathematical Economics, Elsevier, vol. 5(1), pages 43-52, March.
    6. 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.
    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, August.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Giorgio Giorgi, 2019. "Nonnegative Square Matrices: Irreducibility, Reducibility, Primitivity and Some Economic Applications," DEM Working Papers Series 175, University of Pavia, Department of Economics and Management.
    3. PARYS, Wilfried, 2013. "All but one: How pioneers of linear economics overlooked Perron-Frobenius mathematics," Working Papers 2013030, University of Antwerp, Faculty of Business and Economics.
    4. Sah, Raaj, 2000. "Some results for the comparative statics of steady states of higher-order discrete dynamic systems," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1481-1489, September.
    5. Sah, Raaj, 2000. "Some results for the comparative statics of steady states of higher-order discrete dynamic systems," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1481-1489, September.
    6. Kiedrowski, Roman, 2018. "Profit rates equalization and balanced growth in a multi-sector model of classical competition," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 39-53.
    7. Nieuwenhuis, Herman J. & Schoonbeek, Lambert, 1997. "Stability and the structure of continuous-time economic models," Economic Modelling, Elsevier, vol. 14(3), pages 311-340, July.
    8. Giorgio Giorgi & Cesare Zuccotti, 2015. "An Overview on D-stable Matrices," DEM Working Papers Series 097, University of Pavia, Department of Economics and Management.
    9. Pierre Ouellette & Stéphane Vigeant, 2000. "A General Procedure to Recover the Marginal Products of a Cost Minimizing Firm," Journal of Productivity Analysis, Springer, vol. 14(2), pages 143-162, September.
    10. Giorgio Giorgi, 2017. "Various Proofs of the Sylvester Criterion for Quadratic Forms," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 55-66, December.
    11. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    12. Kazuhiro Kurose, 2022. "A two-class economy from the multi-sectoral perspective: the controversy between Pasinetti and Meade–Hahn–Samuelson–Modigliani revisited," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 239-270, April.
    13. Alvarez-Cuadrado, Francisco & Long, Ngo & Poschke, Markus, 2017. "Capital-labor substitution, structural change and growth," Theoretical Economics, Econometric Society, vol. 12(3), September.
    14. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    15. Massimo Cingolani, 2015. "Sylos Labini su Marx: implicazioni per la politica economica (Sylos Labini on Marx: economic policy implications)," Moneta e Credito, Economia civile, vol. 68(269), pages 81-147.
    16. Crettez, Bertrand & Hayek, Naila & Zaccour, Georges, 2023. "When is frugality optimal?," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 65-75.
    17. Fritz, Oliver M. & Sonis, Michael & Hewings, Geoffrey J. D., 1998. "A Miyazawa analysis of interactions between polluting and non-polluting sectors," Structural Change and Economic Dynamics, Elsevier, vol. 9(3), pages 289-305, September.
    18. Pierre‐Richard Agénor, 2011. "Schooling and Public Capital in a Model of Endogenous Growth," Economica, London School of Economics and Political Science, vol. 78(309), pages 108-132, January.
    19. Keiran Sharpe, 2006. "Effective demand in a stylised Keynesian model of growth," Review of Political Economy, Taylor & Francis Journals, vol. 18(2), pages 173-191.
    20. Rodolfo Signorino, 2003. "Book Reviews," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 10(2), pages 339-370.

    More about this item

    Keywords

    M-matrices; K-matrices; Z-matrices; Leontief input-output models; linear economic models;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pav:demwpp:demwp0206. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alice Albonico (email available below). General contact details of provider: https://edirc.repec.org/data/dppavit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.