semidefiniteness

[/ˌsɛmiˈdɛfɪnɪtnəs/]
noun
semidefinitude
1. The quality or state of being semidefinite; in mathematics, the property of a matrix or quadratic form where all eigenvalues are non-negative (positive semidefinite) or non-positive (negative semidefinite)
The semidefiniteness of the covariance matrix ensures that the variance is always non-negative.
A semidefinitude da matriz de covariância garante que a variância seja sempre não-negativa.
2. In linear algebra and optimization, the characteristic of a symmetric matrix having all eigenvalues greater than or equal to zero or less than or equal to zero
Checking for semidefiniteness is crucial in convex optimization problems.
Verificar a semidefinitude é crucial em problemas de otimização convexa.
This is specialized mathematical terminology used primarily in academic and technical contexts in both Brazil and the USA. It is not part of everyday conversation and is restricted to mathematics, engineering, computer science, and physics discussions. In Brazilian universities, both Portuguese and English terms may be used interchangeably depending on the textbook or instructor preference.
Synonyms / Sinônimos
positive semidefinitenessnegative semidefinitenesssemi-definiteness
Antonyms / Antônimos
indefinitenessdefiniteness

Regional Variations

General Brazilian
semidefinitude
Standard mathematical terminology used in academic and technical contexts
Portugal
semidefinitude
Used in Portuguese academic mathematics literature with same meaning
USA
semidefiniteness
Primarily used in English-language mathematics and engineering texts

Related Words

semidefinitepositive definitenegative definiteeigenvaluematrixquadratic formconvex optimization

Related Idioms & Phrases

positive semidefinite matrix
negative semidefinite matrix
test for semidefiniteness
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