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Projective Space


A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the transformations of any group containing G as a subgroup.

A projective space is the space of one-dimensional vector subspaces of a given vector space. For real vector spaces, the notation RP^n or P^n denotes the real projective space of dimension n (i.e., the space of one-dimensional vector subspaces of R^(n+1)) and CP^n denotes the complex projective space of complex dimension n (i.e., the space of one-dimensional complex vector subspaces of C^(n+1)). P^n can also be viewed as the set consisting of R^n together with its points at infinity.


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Cite this as:

Weisstein, Eric W. "Projective Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProjectiveSpace.html

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