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Wat (wie) is basis$7098$ - definitie

ELEMENT OF A BASIS FOR A FUNCTION SPACE

Basis Function; Basis functions; Blending function; Basis Functions; Fourier basis

Standard basis

BASIS OF EUCLIDEAN SPACE CONSISTING OF ONE-HOT VECTORS

Standard bases; Standard basis vector; Kronecker basis; Standard unit vector

In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as \mathbb{R}^n or \mathbb{C}^n) is the set of vectors whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane \mathbb{R}^2 formed by the pairs of real numbers, the standard basis is formed by the vectors

https://en.wikipedia.org/wiki/Standard_basis

Basis (universal algebra)

STRUCTURE INSIDE OF SOME (UNIVERSAL) ALGEBRAS, WHICH ARE CALLED FREE ALGEBRAS. IT GENERATES ALL ALGEBRA ELEMENTS FROM ITS OWN ELEMENTS BY THE ALGEBRA OPERATIONS IN AN INDEPENDENT MANNER

Basis (Universal Algebra)

In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner.

https://en.wikipedia.org/wiki/Basis_(universal_algebra)

Dual basis

BASIS ON A DUAL VECTOR SPACE CANONICALLY ASSOCIATED TO A BASIS ON THE ORIGINAL VECTOR SPACE

Reciprocal basis

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), the dual set of B is a set B∗ of vectors in the dual space V∗ with the same index set I such that B and B∗ form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V∗.

https://en.wikipedia.org/wiki/Dual_basis

Wikipedia

Basis function

In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).

https://en.wikipedia.org/wiki/Basis function