Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
algebraic basis
|
| gptkbp:appliesTo |
gptkb:Vector
|
| gptkbp:cardinality |
equal to the dimension of the vector space
|
| gptkbp:contrastsWith |
gptkb:Schauder_basis
|
| gptkbp:definedIn |
a basis of a vector space over a field such that every element can be written uniquely as a finite linear combination of basis elements
|
| gptkbp:example |
the set of standard unit vectors in R^n is a Hamel basis for R^n
|
| gptkbp:existsIn |
every vector space
|
| gptkbp:field |
linear algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hamel basis
|
| gptkbp:namedAfter |
gptkb:Georg_Hamel
|
| gptkbp:property |
requires the axiom of choice for existence in infinite-dimensional spaces
elements are linearly independent every vector space has a Hamel basis spans the vector space not necessarily countable in infinite-dimensional spaces |
| gptkbp:usedIn |
gptkb:set_theory
functional analysis infinite-dimensional vector spaces |
| gptkbp:bfsParent |
gptkb:Zorn's_Lemma
|
| gptkbp:bfsLayer |
6
|