n-dimensional Euclidean space

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Euclidean_space gptkb:Vector gptkb:normed_vector_space gptkb:topology
gptkbp:automorphismGroup	gptkb:Euclidean_group
gptkbp:basisFor	standard basis
gptkbp:coordinates	Cartesian coordinates
gptkbp:dimensions	n
gptkbp:fieldOfScalars	real numbers
gptkbp:generalizes	Euclidean plane Euclidean 3-space
gptkbp:hasConnection	true
gptkbp:hasInnerProduct	dot product
gptkbp:hasNorm	Euclidean norm
gptkbp:hasSpecialCase	gptkb:Hilbert_space gptkb:normed_vector_space gptkb:topology gptkb:Riemannian_manifold gptkb:finite-dimensional_Hilbert_space inner product space topological vector space real coordinate space finite-dimensional Banach space finite-dimensional metric space finite-dimensional normed vector space finite-dimensional real vector space flat manifold real affine space real vector space
gptkbp:hasSubgroup	gptkb:aircraft gptkb:street hyperplane affine subspace linear subspace
https://www.w3.org/2000/01/rdf-schema#label	n-dimensional Euclidean space
gptkbp:includesMetric	Euclidean distance
gptkbp:isBanachSpace	true
gptkbp:isFiniteDimensional	true
gptkbp:isHilbertSpace	true
gptkbp:isHomogeneous	true
gptkbp:isIsotropic	true
gptkbp:isParacompact	true
gptkbp:isSeparable	true
gptkbp:numberOfIssues	true
gptkbp:symbol	R^n
gptkbp:usedIn	gptkb:geometry gptkb:machine_learning computer science engineering physics statistics
gptkbp:bfsParent	gptkb:Pythagorean_theorem_(generalized) gptkb:orthogonal_group
gptkbp:bfsLayer	5