2026-02-242026-02-242025-12-22https://repositorio.ifal.edu.br/handle/123456789/1409This work aims to present a formal deduction of Sylvester’s criterion, a fundamental theorem in the analysis of the definiteness of quadratic forms associated with real symmetric matrices. The study is structured around the formal development of the criterion, its geometric interpretation, and classical applications. The approach emphasizes the connection between theory and practice, offering suggestions for exploring the content in the classroom through concrete and technological resources.ptAttribution 3.0 BrazilMatemáticaCritério de SylvesterFormas quadráticasMatrizes simétricasSylvester’s CriterionQuadratic formsSymmetric matricesTrabalho de Conclusão de CursoCIENCIAS EXATAS E DA TERRA::MATEMATICA