quadratic form
A "quadratic form" is a fundamental concept in mathematics, especially in algebra and statistics, involving expressions where variables are raised to the second power.
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Definition
C1Algebra
(technical, academic)A polynomial where each term is of degree two in a given number of variables.
Example
- The expression x² + 5xy + y² is a quadratic form in the variables x and y.
C1Linear Algebra
(technical, academic)A function that maps a vector to a scalar, typically represented as xáµ€Ax, where x is a vector and A is a symmetric matrix.
Example
- The quadratic form xáµ€Ax can be used to describe the curvature of surfaces.
C1Statistics
(technical, academic)A scalar quantity expressed as εᵀΛε, where ε is a vector of random variables and Λ is a symmetric matrix.
Example
- In multivariate statistics, quadratic forms are used to test hypotheses about mean vectors.
Similar
Terms that have similar or relatively close meanings to "quadratic form":
multilinear formechelon formclosed formin formabsolute formnormal form