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Projective Space

Basic definition

Projective space is the generalization of the projective plane to more than two dimensions.

Detailed definition

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 R P^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 C P^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.

Related term

projective plane

Educational grade level

college level

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