negative semidefinite

[/ˈnɛɡətɪv ˌsɛmiˈdɛfɪnət/]
adjective
semidefinida negativa
1. In linear algebra and mathematics, describing a matrix or quadratic form where all eigenvalues are less than or equal to zero, and the quadratic form produces non-positive values for all non-zero vectors
A matrix is negative semidefinite if x^T A x ≤ 0 for all vectors x.
Uma matriz é semidefinida negativa se x^T A x ≤ 0 para todos os vetores x.
2. Describing a property of functions in optimization and calculus where the Hessian matrix is negative semidefinite, indicating a concave function
The optimization problem requires the objective function to be negative semidefinite at the critical point.
O problema de otimização requer que a função objetivo seja semidefinida negativa no ponto crítico.
This is a specialized mathematical term used primarily in academic and professional contexts in both Brazil and Portugal. There is no colloquial or slang usage. The term is fundamental in linear algebra, optimization theory, and advanced mathematics courses taught in universities across Portuguese-speaking countries.
Synonyms / Sinônimos
non-positive definiteconcavenegative semi-definite
Antonyms / Antônimos
positive semidefinitepositive definite

Regional Variations

General Brazilian Portuguese
semidefinida negativa
Standard mathematical terminology used in academic and technical contexts
Portugal
semidefinida negativa
Same terminology as Brazilian Portuguese; consistent across Portuguese-speaking mathematical communities

Related Words

eigenvaluematrixquadratic formHessian matrixconcave functionconvex functionsemidefinitenesslinear algebra

Related Idioms & Phrases

negative semidefinite matrix
negative semidefinite operator
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