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gptkbp:instanceOf
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gptkb:mathematical_concept
Function
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gptkbp:alsoKnownAs
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Linear fractional transformation
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gptkbp:application
|
gptkb:Physics
gptkb:geometry
Engineering
Dynamical systems
Conformal mapping
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gptkbp:canBeComposed
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Other Möbius transformations
|
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gptkbp:category
|
gptkb:Projective_geometry
Functions of a complex variable
Conformal maps
|
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gptkbp:condition
|
ad - bc ≠ 0
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gptkbp:definedIn
|
Extended complex plane
|
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gptkbp:designer
|
gptkb:Möbius_transformation
|
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gptkbp:field
|
Complex analysis
|
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gptkbp:fixes
|
At most two points
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gptkbp:form
|
f(z) = (az + b) / (cz + d)
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gptkbp:hasInvariant
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gptkb:Cross-ratio
|
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gptkbp:hasSpecialCase
|
translator
Inversion
Rotation
Dilation
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Möbius Transformation
|
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gptkbp:mapType
|
gptkb:Riemann_sphere
|
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gptkbp:namedAfter
|
gptkb:August_Ferdinand_Möbius
|
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gptkbp:parameter
|
a, b, c, d complex numbers
|
|
gptkbp:preserves
|
gptkb:Angles
Circles
Lines
|
|
gptkbp:relatedGroup
|
gptkb:Projective_linear_group_PGL(2,_C)
|
|
gptkbp:type
|
Rational function
Bijection
|
|
gptkbp:usedIn
|
gptkb:Stereographic_projection
gptkb:Hyperbolic_geometry
Complex dynamics
|
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gptkbp:bfsParent
|
gptkb:Conformal_Mapping
|
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gptkbp:bfsLayer
|
7
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