Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A set of vectors in a vector space V that is linearly independent and spans V.
|
| gptkbp:example |
gptkb:standard_basis_of_R^n
orthonormal basis |
| gptkbp:field |
linear algebra
vector space theory |
| gptkbp:generalizes |
gptkb:Hamel_basis
gptkb:Schauder_basis |
| gptkbp:hasAxiom |
A vector space has a basis (requires the axiom of choice for infinite-dimensional spaces).
|
| https://www.w3.org/2000/01/rdf-schema#label |
basis (mathematics)
|
| gptkbp:property |
A basis is not unique.
Every vector in the vector space can be written uniquely as a linear combination of basis vectors. All bases of a finite-dimensional vector space have the same number of elements. A basis of an infinite-dimensional vector space may be infinite. A vector space may have infinitely many different bases. |
| gptkbp:relatedTo |
gptkb:Vector
gptkb:Gram-Schmidt_process gptkb:dimension_(mathematics) gptkb:Zorn's_lemma linear independence free module Fourier basis polynomial basis basis function basis theorem basis transformation canonical basis coordinate vector dual basis eigenbasis frame (linear algebra) module (mathematics) ordered basis orthogonal basis spanning set wavelet basis |
| gptkbp:usedIn |
coordinate systems
change of basis matrix representation of linear transformations |
| gptkbp:bfsParent |
gptkb:Schauder_basis
|
| gptkbp:bfsLayer |
7
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