positive semidefinite

[/ˈpɑːzətɪv ˌsɛmɪˈdɛfɪnət/]
adjective
semidefinida positiva
1. In linear algebra and matrix theory, describing a square matrix or quadratic form where all eigenvalues are non-negative, or equivalently, where the quadratic form is non-negative for all vectors
A covariance matrix must be positive semidefinite to represent a valid probability distribution.
Uma matriz de covariância deve ser semidefinida positiva para representar uma distribuição de probabilidade válida.
2. A mathematical property ensuring that a bilinear form produces non-negative values for all input vectors in its domain
The Gramian matrix is positive semidefinite by construction.
A matriz de Gram é semidefinida positiva por construção.
This is a technical mathematical term used primarily in academic, engineering, and scientific contexts. It is not subject to regional variation in meaning and is understood uniformly across English-speaking countries and Portuguese-speaking communities. The term is essential in optimization theory, control systems, and machine learning, particularly in convex optimization and covariance matrix analysis.
Synonyms / Sinônimos
nonnegative definitepositive semi-definitePSD (abbreviation)
Antonyms / Antônimos
positive definitenegative semidefiniteindefinite

Regional Variations

General Brazilian Portuguese
semidefinida positiva
Standard term used in mathematics and engineering education
São Paulo
semidefinida positiva
Commonly used in academic and technical contexts
Portugal
semidefinida positiva
Standard usage in Portuguese mathematics; sometimes written as 'semi-definida positiva'

Related Words

eigenvaluequadratic formmatrixsemidefinite programmingGramian matrixcovariance matrixpositive definitedefiniteness

Related Idioms & Phrases

positive semidefinite matrix
positive semidefinite cone
testing for positive semidefiniteness
Look up more words on Fala2Me
The free English-Portuguese dictionary with real Brazilian accents, NYC slang, conjugator and more
Open Fala2Me →