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LEADING PRINCIPAL MINORS AND SEMIDEFINITENESS
Author(s) -
Mandy David M.
Publication year - 2018
Publication title -
economic inquiry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.823
H-Index - 72
eISSN - 1465-7295
pISSN - 0095-2583
DOI - 10.1111/ecin.12536
Subject(s) - hessian matrix , positive definite matrix , principal (computer security) , mathematics , duality (order theory) , mathematical economics , matrix (chemical analysis) , regular polygon , extant taxon , sign (mathematics) , combinatorics , computer science , mathematical analysis , eigenvalues and eigenvectors , physics , materials science , geometry , quantum mechanics , evolutionary biology , composite material , biology , operating system
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)