Sylvester's Minorant Criterion, Lagrange-Beltrami Identity, and Nonnegative Definiteness

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dc.creatorGhorpade, Sudhir R.
dc.creatorLimaye, Balmohan V.
dc.date2007-07-19
dc.date.accessioned2026-07-07T09:56:44Z
dc.date.available2026-07-07T09:56:44Z
dc.descriptionWe consider the characterizations of positive definite as well as nonnegative definite quadratic forms in terms of the principal minors of the associated symmetric matrix. We briefly review some of the known proofs, including a classical approach via the Lagrange-Beltrami identity. For quadratic forms in up to 3 variables, we give an elementary and self-contained proof of Sylvester's Criterion for positive definiteness as well as for nonnegative definiteness. In the process, we obtain an explicit version of Lagrange-Beltrami identity for ternary quadratic forms.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/0707.2885
dc.identifierhttp://arxiv.org/abs/0707.2885
dc.identifierThe Mathematics Student. Special Centenary Volume (2007), 123--130.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167080
dc.subjectHistory and Overview
dc.subjectGeneral Mathematics
dc.subject15A57; 15A15; 15A63; 15A18; 11E25
dc.titleSylvester's Minorant Criterion, Lagrange-Beltrami Identity, and Nonnegative Definiteness
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