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Projective Space

A Space which 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 1-D Vector Subspaces of a given Vector Space. For Real Vector Spaces, the Notation $\Bbb{RP}^n$ or $\Bbb{P}^n$ denotes the Real projective space of dimension $n$ (i.e., the Space of 1-D Vector Subspaces of $\Bbb{R}^{n+1}$) and $\Bbb{CP}^n$ denotes the Complex projective space of Complex dimension $n$ (i.e., the space of 1-D Complex Vector Subspaces of $\Bbb{C}^{n+1}$). $\Bbb{P}^n$ can also be viewed as the set consisting of $\Bbb{R}^n$ together with its Points at Infinity.

© 1996-9 Eric W. Weisstein