Abstract projective space

Projective correlation

A correlation of a projective space S is a Collineätion 𝛼 :S →S𝐨𝐩 into the Dual projective space. geo

Further terminology

• A correlation which is an involution is a polarity.
• The image of a point 𝑃 under a polarity 𝛼 is called the polar (hyperplane) 𝑃𝛼, while the image of a hyperplane H is called the pole (point) H𝛼.
• If 𝑃I𝑄𝛼 then 𝑃 and 𝑄 are conjugate, if 𝑃I𝑃𝛼 it is self-conjugate.

Examples

• Orthogonal complement polarity

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