Complex projective line

English

Noun

1. Template:Lb A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); Template:Lb the set of equivalence classes of ordered pairs (α, β) of complex numbers, not both zero, with respect to the equivalence relation "(α, β) ≡ (λα, λβ) for all nonzero complex λ".
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Usage notes

• The formal definition above is a version of the definition of a projective space by homogeneous coordinates. (See also Template:Pedia)
• Notations include: $\mathbb{P}({ℂ}^2),{\mathbb{P}}_1(ℂ)\text{ and }ℂ{\mathbb{P}}^1$.

Synonyms

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Translations

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See also

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Further reading

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• Projective straight line on Template:W