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finite-dimensional Euclidean space
URI:
https://gptkb.org/entity/finite-dimensional_Euclidean_space
GPTKB entity
Statements (47)
Predicate
Object
gptkbp:instanceOf
gptkb:Vector
gptkb:mathematical_concept
gptkb:topology
inner product space
gptkbp:basisFor
orthonormal basis
gptkbp:coordinates
gptkb:polar_coordinates_(in_2D)
gptkb:spherical_coordinates_(in_3D)
Cartesian coordinates
gptkbp:dimensions
finite
gptkbp:generalizes
Euclidean line
Euclidean plane
Euclidean 3-space
gptkbp:hasConnection
yes
gptkbp:hasDistanceFunction
Euclidean distance
gptkbp:hasInnerProduct
yes
gptkbp:hasNorm
yes
gptkbp:hasSpecialCase
gptkb:Hilbert_space
gptkb:normed_vector_space
gptkb:topology
inner product space
gptkbp:hasStandardExample
R^n
gptkbp:hasSubgroup
real coordinate space
gptkbp:hasTopology
gptkb:Euclidean_topology
https://www.w3.org/2000/01/rdf-schema#label
finite-dimensional Euclidean space
gptkbp:isContrastWith
gptkb:Euclidean_space
gptkb:Hilbert_space
gptkb:complex_vector_space
gptkbp:isHausdorff
yes
gptkbp:isHomogeneous
yes
gptkbp:isLocallyCompact
yes
gptkbp:isParacompact
yes
gptkbp:isPathConnected
yes
gptkbp:isSecondCountable
yes
gptkbp:isSeparable
yes
gptkbp:namedAfter
gptkb:Euclid
gptkbp:numberOfIssues
yes
gptkbp:symmetry
gptkb:Euclidean_group
orthogonal group
gptkbp:usedIn
gptkb:geometry
gptkb:machine_learning
computer science
engineering
physics
statistics
linear algebra
gptkbp:bfsParent
gptkb:Hilbert_space
gptkbp:bfsLayer
4