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

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

homographies, linear fractional transformations, bilinear transformations, and spin transformations (in relativity theory). Möbius transformations are defined...

linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function...

the proof. If f ( x ) {\displaystyle f(x)} is given by the linear fractional transformation f ( x ) = ( cos ⁡ α ) x − sin ⁡ α ( sin ⁡ α ) x + cos ⁡ α ...

projective transformations, homographies, or linear fractional transformations. They form the projective linear group PGL(2, R). Each element of PGL(2, R)...

cases in which w = f(z) is a constant. The linear fractional transformation, also known as a Möbius transformation, has many fascinating properties. Four...

{\displaystyle z\mapsto {\frac {za+b}{zc+d}}\ ,} but otherwise the linear fractional transformation is seen as an equivalence: U [ z a + b ,   z c + d ] ∼ U [...

one, then there are exactly zero or one positive roots. A linear fractional transformation of the variable makes it possible to use the rule of signs...

in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It...

(also called linear fractional transformations), with the understanding that when the denominator of the linear fractional transformation is 0, the image...

fractional Fourier, Laplace, Gauss–Weierstrass, Bargmann and the Fresnel transforms as particular cases. The name "linear canonical transformation" is...

variable linear fractional transformations just as circular angle is preserved by the Möbius transformations of the ordinary complex plane. Transformations preserving...

PSL(2,R) acts on H {\displaystyle H} by linear fractional transformations (also known as Möbius transformations): ( a b c d ) ⋅ z = a z + b c z + d . {\displaystyle...

taken to be complex numbers, any Möbius transformation is represented by a linear fractional transformation of complex numbers, and the hyperbolic motions...

that is, a discrete subgroup Γ of PSL(2, R), Γ acts on H via linear fractional transformation. Each element of PSL(2, R) in fact defines an isometry of H...

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...

(mathematics). Affine transformation, in geometry Linear transformation between modules in linear algebra. Also called a linear map. Transformation matrix which...

z=F_{\ell }(\mathbf {P} ,\mathbf {K} )\,w} Called the lower linear fractional transformation, F ℓ {\displaystyle F_{\ell }} is defined (the subscript comes...

\ [-20,20]} Results for compositions of linear fractional (Möbius) transformations include the following, as examples: Theorem LFT1 — On...

numbers, and dual numbers. The conformal maps are described by linear fractional transformations in each case. In Riemannian geometry, two Riemannian metrics...

In crystallography, a fractional coordinate system (crystal coordinate system) is a coordinate system in which basis vectors used to the describe the space...

the name anharmonic ratio. The cross-ratio is preserved by linear fractional transformations. It is essentially the only projective invariant of a quadruple...

necessarily centerless). As for Möbius transformations, the group PGL(2, K) can be interpreted as fractional linear transformations with coefficients in K. Points...

Kochina, P. Ya.; Kochina, N. N. (1999). "Some properties of a linear-fractional transformation". Journal of Applied Mathematics and Mechanics. 63 (2): 161–163...

modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli...

Nevertheless, the conformal group in each case is given by linear fractional transformations on the appropriate plane. Given a (Pseudo-)Riemannian manifold...

for a project entitled "continued fraction convergents and linear fractional transformations". O'Dorney started attending Harvard College in 2011, where...

MATLAB. An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in. One of the first applications of the Rosenbrock...

different methodologies to design a LPV controller namely, Linear fractional transformations which relies on the small gain theorem for bounds on performance...