Definition:Cross-Ratio/Complex Analysis
< Definition:Cross-Ratio(Redirected from Definition:Complex Cross-Ratio)
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Definition
Let $z_1, z_2, z_3, z_4$ be distinct complex numbers.
The cross-ratio of $z_1, z_2, z_3, z_4$ is defined and denoted:
- $\paren {z_1, z_3; z_2, z_4} = \dfrac {\paren {z_1 - z_2} \paren {z_3 - z_4} } {\paren {z_1 - z_4} \paren {z_3 - z_2} }$
Also known as
Some sources do not hyphenate cross-ratio, leaving it as: cross ratio.
Also see
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations: Exercise $6$.