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.
Related Idioms & Phrases
positive semidefinite matrix
positive semidefinite cone
testing for positive semidefiniteness
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