Real point

In geometry, a real point is a point in the complex projective plane with homogeneous coordinates (x,y,z) for which there exists a nonzero complex number λ such that λx, λy, and λz are all real numbers.

This definition can be widened to a complex projective space of arbitrary finite dimension as follows:

${\displaystyle (u_{1},u_{2},\ldots ,u_{n})}$

are the homogeneous coordinates of a real point if there exists a nonzero complex number λ such that the coordinates of

${\displaystyle (\lambda u_{1},\lambda u_{2},\ldots ,\lambda u_{n})}$

are all real.

A point which is not real is called an imaginary point.