negative semidefiniteness

[/ˈneɡətɪv ˌsɛmɪˌdɛfɪnɪtˈnɛs/]
nounfemininepl: negative semidefinitenesses
semidefinitidade negativa
1. A property of a square matrix or quadratic form where all eigenvalues are less than or equal to zero, or equivalently, where the matrix produces non-positive results for all non-zero vectors in its domain
The Hessian matrix exhibits negative semidefiniteness, indicating that the function is concave at that point.
A matriz Hessiana exibe semidefinitidade negativa, indicando que a função é côncava naquele ponto.
2. In optimization theory, a condition ensuring that a quadratic form satisfies x^T A x ≤ 0 for all vectors x
We verified negative semidefiniteness of the constraint matrix to confirm the convexity of the optimization problem.
Verificamos a semidefinitidade negativa da matriz de restrição para confirmar a convexidade do problema de otimização.
This is a technical mathematical term used exclusively in academic, engineering, and computational contexts. It is widely recognized in both Brazilian and Portuguese mathematical communities, particularly in optimization, linear algebra, and control theory. The term is identical in usage across English-speaking and Portuguese-speaking countries, with no colloquial variations.
Synonyms / Sinônimos
negative semidefinite propertynon-positive definiteness
Antonyms / Antônimos
positive semidefinitenesspositive definitenessindefiniteness

Regional Variations

General Brazilian Portuguese
semidefinitidade negativa
Standard mathematical terminology used in academic and professional contexts
Portugal
semidefinitude negativa
Alternative Portuguese variant; less commonly used than Brazilian Portuguese version
International/Technical
definitude negativa semiforte
Rare alternative phrasing occasionally found in technical literature

Related Words

eigenvaluequadratic formmatrixconcavityHessian matrixsemidefinite programmingpositive semidefiniteness

Related Idioms & Phrases

to establish negative semidefiniteness
to test for negative semidefiniteness
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