Projective point

A projective point is an equivalence class

[x_{0} : \dots : x_{n}]

of nonzero coordinate vectors under multiplication by a nonzero scalar.

Table of contents
- Homogeneous coordinate Projective point
- Coordinate point Projective point

Homogeneous coordinate

The homogeneous coordinates

[x_{0} : \dots : x_{n}]

of a projective point are defined only up to simultaneous multiplication by a nonzero scalar.

Coordinate point

A coordinate point of

P^{n}

is represented by a standard basis vector, so exactly one of its homogeneous coordinates is nonzero.

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