finite-dimensional Euclidean space

GPTKB entity

AI-created image

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