Source: wikibot/linear-fractional-transformation
= Linear fractional transformation
{wiki=Linear_fractional_transformation}
A linear fractional transformation (LFT), also known as a Möbius transformation, is a function that maps the complex plane to itself. It is defined by the formula: \\\[ f(z) = \\frac\{az + b\}\{cz + d\} \\\] where \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are complex numbers, and \\(ad - bc \\neq 0\\) to ensure that the transformation is well-defined and non-degenerate.