|
gptkbp:instanceOf
|
gptkb:algebraic_geometry
gptkb:mathematical_concept
|
|
gptkbp:can_be_diagonalized
|
Yes
|
|
gptkbp:class
|
By rank of the matrix
By signature of the quadratic form
|
|
gptkbp:defines
|
A quadric is a hypersurface defined as the zero set of a degree-two polynomial in n variables.
|
|
gptkbp:degree
|
2
|
|
gptkbp:dimensions
|
n-1
|
|
gptkbp:equation_form
|
Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0
|
|
gptkbp:example
|
gptkb:Ellipsoid
gptkb:Hyperbola
Cylinder
Cone
Ellipse
Hyperboloid
Paraboloid
|
|
gptkbp:field
|
gptkb:Mathematics
|
|
gptkbp:hasInvariant
|
gptkb:Projective_transformations
Affine transformations
|
|
gptkbp:hasSubfield
|
gptkb:Algebraic_geometry
|
|
gptkbp:in_2D
|
gptkb:Conic_section
|
|
gptkbp:in_3D
|
gptkb:Quadric_surface
|
|
gptkbp:in_higher_dimensions
|
gptkb:Quadric_hypersurface
|
|
gptkbp:matrixRepresentation
|
Symmetric matrix
|
|
gptkbp:relatedConcept
|
gptkb:Affine_variety
gptkb:Projective_variety
gptkb:Algebraic_surface
gptkb:Conic_section
Quadratic form
|
|
gptkbp:studiedBy
|
gptkb:Linear_algebra
gptkb:Analytic_geometry
gptkb:Projective_geometry
|
|
gptkbp:used_in
|
gptkb:Computer_graphics
gptkb:Algebraic_topology
gptkb:CAD
gptkb:Physics
gptkb:Vision
gptkb:robot
gptkb:Differential_geometry
Architecture
Astronomy
Engineering
Statistics
Geodesy
Structural engineering
Optimization
Geometric modeling
|
|
gptkbp:bfsParent
|
gptkb:Meiko_Scientific
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Quadrics
|