quadratic form
[kwɑːˈdrætɪk fɔːrm]
nounpl: quadratic forms
forma quadrática
1. A polynomial expression of degree two in one or more variables, where each term has variables raised to the power of two or is a product of two variables
The quadratic form 3x² + 2xy + 5y² represents a mathematical expression used in linear algebra.
A forma quadrática 3x² + 2xy + 5y² representa uma expressão matemática usada em álgebra linear.
2. In linear algebra, a homogeneous polynomial of degree 2 that can be represented as a matrix equation x^T Ax, where x is a vector and A is a symmetric matrix
The quadratic form can be analyzed to determine if it is positive definite by examining its associated matrix.
A forma quadrática pode ser analisada para determinar se é positiva definida examinando sua matriz associada.
This is a specialized mathematical term used predominantly in academic and technical contexts in both Brazil and Portugal. It is part of standard linear algebra and mathematics curriculum in universities across Portuguese-speaking countries and English-speaking regions. The term has no colloquial variants and maintains consistent usage across regions.
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