finite-dimensional Euclidean space

URI: https://gptkb.org/entity/finite-dimensional_Euclidean_space
GPTKB entity
AI-created image of finite-dimensional Euclidean space
AI-created image
Statements (48)
Predicate Object
gptkbp:instanceOf gptkb:Vector
gptkb:mathematical_concept
gptkb:topology
gptkb: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
gptkb:inner_product_space
gptkbp:hasStandardExample R^n
gptkbp:hasSubgroup real coordinate space
gptkbp:hasTopology gptkb:Euclidean_topology
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
gptkb:orthogonal_group
gptkbp:usedIn gptkb:geometry
gptkb:machine_learning
computer science
engineering
physics
statistics
linear algebra
gptkbp:bfsParent gptkb:Hilbert_spaces
gptkb:inner_product_spaces
gptkbp:bfsLayer 7
https://www.w3.org/2000/01/rdf-schema#label finite-dimensional Euclidean space