Euclidean space

GPTKB entity

Statements (107)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alternativeName affine_space
mathematical_space
pseudo-Euclidean_space
gptkbp:application gptkb:Lorentzian_geometry
spacetime models
gptkbp:basisFor gptkb:Euclidean_geometry
differential geometry
vector calculus
linear algebra
analytic geometry
classical geometry
multivariable calculus
rigid body mechanics
gptkbp:contrastsWith gptkb:Minkowski_space
gptkb:geometry
gptkb:Euclidean_space_(where_the_metric_is_positive-definite)
non-Euclidean space
gptkbp:coordinates Cartesian coordinates
gptkbp:definedIn finite-dimensional real vector space with a non-degenerate, symmetric bilinear form of indefinite signature
gptkbp:describedBy gptkb:basketball
gptkb:butter
gptkb:principal_component_analysis
gptkb:spectral_theorem
gptkb:standard
gptkb:Polygon
gptkb:Gram-Schmidt_process
gptkb:Gram_matrix
gptkb:Metric
inner product
orthogonal complement
orthogonality
orthonormal basis
reflection
translator
affine transformations
angles
areas
axioms of Euclidean geometry
basis vectors
convex set
coordinate systems
cross product
cube
distance formula
distance-preserving maps
dot product
eigenvalues
eigenvectors
hyperplane
lattice
lengths
orthant
orthogonal group
orthogonal projection
orthogonal transformations
principal axes
quadratic form
rotation matrices
scaling
similarity transformations
simplex
subspace
volumes
gptkbp:dimension3 Euclidean 3-space
gptkbp:dimensions Euclidean line
Euclidean plane
n
n = p + q
gptkbp:field gptkb:geometry
gptkb:mathematics
linear algebra
gptkbp:generalizes gptkb:Euclidean_space
gptkbp:hasDistanceFormula distance = sqrt(sum((xi-yi)^2))
gptkbp:hasGroupOfIsometries gptkb:Euclidean_group
gptkbp:hasProperty gptkb:parallelogram_law
gptkb:Pythagorean_theorem
flat geometry
homogeneity
isotropy
rotational invariance
translational invariance
gptkbp:hasSpecialCase gptkb:Hilbert_space
gptkb:Minkowski_space
real coordinate space
gptkbp:hasSubgroup gptkb:Euclidean_space
gptkbp:hasTopology standard topology
https://www.w3.org/2000/01/rdf-schema#label Euclidean space
gptkbp:includesMetric Euclidean metric
gptkbp:namedAfter gptkb:Euclid
gptkbp:property distance squared can be positive, negative, or zero
gptkbp:relatedTo metric tensor
quadratic form
gptkbp:signature (p, q) where p and q are non-negative integers
gptkbp:structure gptkb:Vector
gptkb:topology
inner product space
normed space
gptkbp:used_in gptkb:special_relativity
gptkb:theoretical_physics
gptkbp:usedIn gptkb:geometry
computer science
engineering
physics
gptkbp:bfsParent gptkb:Hilbert_space
gptkb:geometry
gptkbp:bfsLayer 4