IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v9y2017i6p55.html
   My bibliography  Save this article

Various Proofs of the Sylvester Criterion for Quadratic Forms

Author

Listed:
  • Giorgio Giorgi

Abstract

In the first part of the paper we present several proofs of the so-called Sylvester criterion for quadratic forms; some of the said proofs are short and easy. In the second part of the paper we give an algebraic proof of the Sylvester criterion for quadratic forms subject to a linear homogeneous system.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:55
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/70703/38960
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/70703
    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. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    3. Fuad Aleskerov & Hasan Ersel & Dmitri Piontkovski, 2011. "Linear Algebra for Economists," Springer Texts in Business and Economics, Springer, number 978-3-642-20570-5, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giorgio Giorgi, 2022. "A Proof of the Sylvester Criterion for Quadratic Forms via Optimality Conditions for Quadratic Functions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(2), pages 1-1, May.
    2. Giorgi Giorgio, 2018. "A Classroom Note on Twice Continuously Differentiable Strictly Convex and Strongly Quasiconvex Functions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(3), pages 42-52, June.
    3. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.

    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, 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. 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. Paul, Saumik, 2019. "A Decline in Labor's Share with Capital Accumulation and Complementary Factor Inputs: An Application of the Morishima Elasticity of Substitution," IZA Discussion Papers 12219, Institute of Labor Economics (IZA).
    4. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    5. V. Vandenberghe, 2018. "The Contribution of Educated Workers to Firms’ Efficiency Gains: The Key Role of Proximity to the ‘Local’ Frontier," De Economist, Springer, vol. 166(3), pages 259-283, September.
    6. Morrison, Catherine J., 1986. "Productivity measurement with non-static expectations and varying capacity utilization : An integrated approach," Journal of Econometrics, Elsevier, vol. 33(1-2), pages 51-74.
    7. Matteo G. Richiardi & Luis Valenzuela, 2024. "Firm heterogeneity and the aggregate labour share," LABOUR, CEIS, vol. 38(1), pages 66-101, March.
    8. Sébastien Marchand, 2011. "Technical Efficiency, Farm Size and Tropical Deforestation in the Brazilian Amazonian Forest," Working Papers halshs-00552981, HAL.
    9. Managi, Shunsuke & Opaluch, James J. & Jin, Di & Grigalunas, Thomas A., 2006. "Stochastic frontier analysis of total factor productivity in the offshore oil and gas industry," Ecological Economics, Elsevier, vol. 60(1), pages 204-215, November.
    10. Tung Liu, 2020. "Measuring Technical, Allocative inefficiency, and Cost Inefficiency by Applying Duality Theory," Working Papers 202001, Ball State University, Department of Economics, revised Jun 2020.
    11. Antle, John M. & Aitah, Ali S., 1984. "Egypt'S Multiproduct Agricultural Technology And Agricultural Policy," Working Papers 225790, University of California, Davis, Department of Agricultural and Resource Economics.
    12. Krasachat, W., 2000. "Production Structure and Technical Change in Thai Agriculture, 1972-1994," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123688, Australian Agricultural and Resource Economics Society.
    13. T. Gries & R. Grundmann & I. Palnau & M. Redlin, 2017. "Innovations, growth and participation in advanced economies - a review of major concepts and findings," International Economics and Economic Policy, Springer, vol. 14(2), pages 293-351, April.
    14. Renwick, Alan W. & Revoredo-Giha, Cesar & Reader, Mark A., 2005. "Uk Sugar Beet Farm Productivity Under Different Reform Scenarios: A Farm Level Analysis," Environmental Economy and Policy Research Discussion Papers 31936, University of Cambridge, Department of Land Economy.
    15. Bailey, Alastair & Irz, Xavier T. & Balcombe, Kelvin George, 2003. "An Appliation Of The Stochastic Latent Variable Approach To The Correction Of Sector Level Tfp Calculations In The Face Of Biased Technological Change," 2003 Annual Meeting, August 16-22, 2003, Durban, South Africa 25842, International Association of Agricultural Economists.
    16. Julien Daubanes & Pierre Lasserre, 2019. "The supply of non-renewable resources," Canadian Journal of Economics, Canadian Economics Association, vol. 52(3), pages 1084-1111, August.
    17. Moschini, G. & Moro, D., 1993. "A Food demand System for Canada," Papers 1-93, Gouvernement du Canada - Agriculture Canada.
    18. Håvard Hungnes, 2016. "Using common factors to identify substitution possibilities in a factor demand system with technological changes," Discussion Papers 849, Statistics Norway, Research Department.
    19. Henry-Jean GATHON & Sergio PERELMAN, 1989. "Etude Comparative Des Performances Des Societes De Chemins De Fer," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 60(1), pages 61-80, January.
    20. Sadorsky, P. A., 1989. "Measuring Resource Scarcity in Non-renewable Resources with Inequality Constrained Estimation," Queen's Institute for Economic Research Discussion Papers 275216, Queen's University - Department of Economics.

    More about this item

    Keywords

    Quadratic forms; Sylvester criterion; positive definite quadratic forms; constrained quadratic forms.;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:jmrjnl:v:9:y:2017:i:6:p:55. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.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.