negative definite

[/ˈnɛɡətɪv ˈdɛfɪnət/]
adjective
definida negativa
1. In mathematics and linear algebra, describing a matrix or quadratic form where all eigenvalues are negative, or where the form always produces negative values for any non-zero vector
A negative definite matrix ensures that the quadratic form yields only negative values for all non-zero input vectors.
Uma matriz definida negativa garante que a forma quadrática produza apenas valores negativos para todos os vetores de entrada não-nulos.
2. In optimization theory, referring to a function that has a unique maximum point and is bounded above
The negative definite Hessian matrix indicates that the critical point is a local maximum.
A matriz Hessiana definida negativa indica que o ponto crítico é um máximo local.
This is a specialized mathematical and scientific term used uniformly across English-speaking and Portuguese-speaking academic communities. It has no colloquial usage and appears primarily in higher mathematics, linear algebra, optimization theory, and engineering contexts. The term is technical and formal in both English and Portuguese.
Synonyms / Sinônimos
negative-definitestrictly negative definiteentirely negative
Antonyms / Antônimos
positive definitepositive semi-definiteindefinite

Regional Variations

General Brazilian
definida negativa
Standard mathematical terminology used in universities and technical contexts
Portugal
definida negativa
Same terminology used in Portuguese academic mathematics
General English-speaking
negative definite
Exclusively used in mathematical and scientific contexts

Related Words

eigenvaluequadratic formmatrixHessian matrixsemi-definitepositive definitesymmetric matrix
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