Complex projective space

Parallel lines in the plane intersect at the vanishing point in the line at infinity.

In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account). Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously as P(C), P_n(C) or CP. When n = 1, the complex projective space CP is the Riemann sphere, and when n = 2, CP is the complex projective plane (see there for a more elementary discussion).

单词	Complex projective space
释义	Complex projective space 英语百科 Complex projective space In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account). Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously as P(C), P_n(C) or CP. When n = 1, the complex projective space CP is the Riemann sphere, and when n = 2, CP is the complex projective plane (see there for a more elementary discussion).
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