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A projective basis is + points in general position, in a projective space of dimension n. A convex basis of a polytope is the set of the vertices of its convex hull. A cone basis [5] consists of one point by edge of a polygonal cone. See also a Hilbert basis (linear programming).
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.
By definition, every σ-algebra, every filter (and so in particular, every neighborhood filter), and every topology is a covering π-system and so also a base for a topology. In fact, if Γ is a filter on X then { ∅ } ∪ Γ is a topology on X and Γ is a basis for it. A base for a topology does not have to be closed under finite ...
In mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent.Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.
Even if it is possible to devise a specific way to remove vectors from the set until it becomes a basis, this approach may become unfeasible in practice if the set is large or infinite. In some applications, it may be an advantage to use more vectors than necessary to represent v {\displaystyle \mathbf {v} } .
In mathematics, an ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence of n scalars called coordinates.
In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context: . In a coordinate space, and more generally in a free module, it refers to the standard basis defined by the Kronecker delta.
Every vector a in three dimensions is a linear combination of the standard basis vectors i, j and k.. In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. [1]