polynomial basis
A "polynomial basis" is a fundamental concept in algebra and numerical analysis, used to represent and manipulate polynomials efficiently.
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Definition
C1Vector Spaces
(technical, academic)A set of polynomials that are linearly independent and can represent any polynomial in the space as a linear combination.
Example
- The set {1, x, x^2} forms a polynomial basis for the space of quadratic polynomials.
C2Finite Fields
(technical, academic)A basis for an extension field where elements are represented as polynomials with coefficients from a base field.
Example
- In a Galois field, a polynomial basis is used to perform arithmetic operations efficiently.
C1Numerical Analysis
(technical, academic)A set of polynomials used to represent functions or data points for operations like interpolation and approximation.
Example
- Chebyshev polynomials are often used as a polynomial basis for approximating functions.
Similar
Terms that have similar or relatively close meanings to "polynomial basis":
primitive polynomialpolynomial timecharacteristic polynomialminimal polynomialbinomial series