fractionallinear

Fractional linear is a term that can refer to several related mathematical concepts. Most commonly, it relates to fractional linear transformations, also known as Möbius transformations or simply linear fractional transformations. These are functions of the form f(z) = (az + b) / (cz + d), where a, b, c, and d are complex numbers and ad - bc is non-zero. These transformations are fundamental in complex analysis and geometry, particularly in the study of the Riemann sphere. They map circles and lines to circles and lines, and they form a group under composition.

The term fractional linear might also, in a broader sense, allude to operations or expressions involving fractions where linear components are present. This could appear in areas like linear algebra or calculus where fractional exponents or coefficients are used in linear equations or functions. However, without further context, the primary association of "fractional linear" is with the transformations described above. Their geometric properties and algebraic structure make them a cornerstone of various advanced mathematical disciplines.