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Various Proofs of the Sylvester Criterion for Quadratic Forms

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  • 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
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    References listed on IDEAS

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    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, April.
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    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.

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    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

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