Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [linear-fractional-transformation]

For questions about linear fractional transformations.

A linear fractional transformation (l.f.t.) is a function of the form $f(z)=\dfrac{az+b}{cz+d}$, where $a,b,c,d\in\mathbb C$. The set of all such functions is closed under composition and inversion. It is a non-abelian group.

47 questions
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Is the image of the open disk under a linear-fractional transformation always a Caratheodory Domain?

I am not enough of a complex analyst to understand well the definition of Caratheodory Domain... It seems to me that set with a boundary that looks like a small deformation of a circle or loop would fit the description. If I take a linear-fractional…
Derek Thompson
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Which LFT is right?

The question is, Find an LFT that maps |z|<=1 onto |w|<=1 so that z=i/2 is mapped onto w=0. Sketch the images of the lines x=const and y=const. By searching and solving, I found several different…
J sw
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Converting a Linear Fractional Transformation as a Hyperbola

I'm trying to show algebraically that a Linear Fractional Transformation of the form $$f(x)=\frac{(ax+b)}{(cx+d)}$$ can be written as hyperbolas of the form $$(x-h)(y-k)=m$$ I started by expanding the hyperbola equation to get $$xy-hy-kx+hk=m$$ and…
Luke DeLong
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