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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
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gptkbp:can_be_diagonalized
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Yes
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gptkbp:class
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By rank of the matrix
By signature of the quadratic form
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gptkbp:defines
|
A quadric is a hypersurface defined as the zero set of a degree-two polynomial in n variables.
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gptkbp:degree
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2
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gptkbp:dimensions
|
n-1
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gptkbp:equation_form
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Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0
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gptkbp:example
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gptkb:Ellipsoid
gptkb:Hyperbola
Cylinder
Cone
Ellipse
Hyperboloid
Paraboloid
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gptkbp:field
|
gptkb:Mathematics
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gptkbp:hasInvariant
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gptkb:Projective_transformations
Affine transformations
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gptkbp:hasSubfield
|
gptkb:Algebraic_geometry
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Quadrics
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gptkbp:in_2D
|
Conic section
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gptkbp:in_3D
|
Quadric surface
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gptkbp:in_higher_dimensions
|
gptkb:Quadric_hypersurface
|
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gptkbp:matrixRepresentation
|
Symmetric matrix
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gptkbp:relatedConcept
|
gptkb:Affine_variety
gptkb:Projective_variety
Algebraic surface
Conic section
Quadratic form
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gptkbp:studiedBy
|
gptkb:Linear_algebra
gptkb:Analytic_geometry
gptkb:Projective_geometry
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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
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gptkbp:bfsParent
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gptkb:Meiko_Scientific
gptkb:GASNet
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gptkbp:bfsLayer
|
7
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