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Leading Principal Minors And Semidefiniteness

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  • David M. Mandy

Abstract

Semidefinite matrices often arise in economic models, usually as Hessian matrices of convex or concave functions. Anytime the matrix can be semidefinite, rather than definite, the task of characterizing it is burdensome because extant results require that all principal minors be signed. A theorem is presented that shows it is sufficient to sign only selected principal minors when the matrix has a definite submatrix. This theorem is particularly useful in duality applications. The theorem also provides relatively easy proof of the standard relationship between semidefiniteness and principal minors. (JEL C02)

Suggested Citation

  • David M. Mandy, 2018. "Leading Principal Minors And Semidefiniteness," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1396-1398, April.
    • Handle: RePEc:bla:ecinqu:v:56:y:2018:i:2:p:1396-1398
    DOI: 10.1111/ecin.12536
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    References listed on IDEAS

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    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293.
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    Cited by:

    1. David M. Kaplan & Longhao Zhuo, 2015. "Bayesian and frequentist inequality tests," Working Papers 1516, Department of Economics, University of Missouri, revised Feb 2018.
    2. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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