composed of homothety and isometry, and is called a conformal linear transformation. Applications of conformal mapping exist in aerospace engineering, in biomedical...

The Lie group of these transformations has been called the conformal orthogonal group, the conformal linear transformation group or the homogeneous...

special conformal transformation is a linear fractional transformation that is not an affine transformation. Thus the generation of a special conformal transformation...

In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle...

linear isometry also necessarily preserves angles, therefore a linear isometry transformation is a conformal linear transformation. Examples A linear...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

Möbius transformation. "Quasi-conformal mapping", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Conformal maps gallery Weisstein, Eric W. "Linear Fractional...

of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: The conformal orthogonal...

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional...

in 1850, is a rigidity theorem about conformal mappings in Euclidean space. It states that every smooth conformal mapping on a domain of Rn, where n >...

automorphisms of V {\displaystyle V} , i.e. the set of all bijective linear transformations V → V {\displaystyle V\to V} , together with functional composition...

of France) Isometry Similarity Affine transformation Projective transformation Inversion Conformal transformations preserve angles, and are, in the first...

"Z" reflects that the scalar transformations form the center of the general linear group. The projective special linear group, PSL, is defined analogously...

conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry...

A conformal linear transformation preserves angles and distance ratios, meaning that transforming orthogonal vectors by the same conformal linear transformation...

A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical...

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that...

two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations. In...

series may be linear sequence transformations or non-linear sequence transformations. In general, the non-linear sequence transformations tend to be more...

In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian...

Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp...

readable introduction to the concept of conformal infinity plus examples. Frauendiener, Jörg (2004). "Conformal Infinity". Living Reviews in Relativity...

and medical imaging. Computational quasi-conformal geometry has been developed, which extends the quasi-conformal theory into a discrete setting. It has...

nonlinear conformal ("angle preserving") transformations. One has Lorentz transformations ⊂ Poincaré transformations ⊂ conformal group transformations. Some...

role in the conformal geometry of Riemannian manifolds. In particular, it can be used to show that if the metric is rescaled by a conformal factor of ⁠...

In conformal geometry, a conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called...

characterized as the group of volume and orientation preserving linear transformations of R n {\displaystyle \mathbb {R} ^{n}} . This corresponds to the...

called Möbius transformations. These correspond precisely with those bijections of the Riemann sphere that preserve orientation and are conformal. In the study...

group. Lorentz transformations are examples of linear transformations; general isometries of Minkowski spacetime are affine transformations. Assume two inertial...

of the plane which preserve the half-plane; these are conformal, circle-preserving transformations which send the ⁠ x {\displaystyle x} ⁠-axis to itself...