Finite-Dimensional Vector Spaces
GPTKB entity
Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:geometry
computer science physics matrix theory systems of linear equations |
| gptkbp:basisExists |
true
|
| gptkbp:contrastsWith |
Infinite-dimensional vector spaces
|
| gptkbp:dimensions |
finite
|
| gptkbp:example |
gptkb:Euclidean_space
R^n C^n space of polynomials of degree ≤ n |
| gptkbp:hasProperty |
all norms are equivalent
dimension is the number of basis elements dual space is also finite-dimensional every basis has same number of elements every linear operator has a matrix representation finite basis can be extended to a basis finite generating set contains a basis isomorphic to coordinate space linear maps can be represented by matrices quotient spaces are finite-dimensional rank-nullity theorem applies subspaces are finite-dimensional finite-dimensionality is preserved under isomorphism |
| https://www.w3.org/2000/01/rdf-schema#label |
Finite-Dimensional Vector Spaces
|
| gptkbp:studiedIn |
gptkb:Linear_algebra
|
| gptkbp:subclassOf |
gptkb:Vector
|
| gptkbp:bfsParent |
gptkb:Paul_Halmos
|
| gptkbp:bfsLayer |
4
|