Editing Projective space (section)

=== Span ===
Every [[set intersection|intersection]] of projective subspaces is a projective subspace. It follows that for every subset {{mvar|S}} of a projective space, there is a smallest projective subspace containing {{mvar|S}}, the intersection of all projective subspaces containing {{mvar|S}}. This projective subspace is called the ''projective span'' of {{mvar|S}}, and {{mvar|S}} is a spanning set for it.

A set {{mvar|S}} of points is ''projectively independent'' if its span is not the span of any proper subset of {{mvar|S}}. If {{mvar|S}} is a spanning set of a projective space {{mvar|P}}, then there is a subset of {{mvar|S}} that spans {{mvar|P}} and is projectively independent (this results from the similar theorem for vector spaces). If the dimension of {{mvar|P}} is {{mvar|n}}, such an independent spanning set has {{math|''n'' + 1}} elements.

Contrarily to the cases of [[vector space]]s and [[affine space]]s, an independent spanning set does not suffice for defining coordinates. One needs one more point, see next section.