LEADING PRINCIPAL MINORS AND SEMIDEFINITENESS

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)