Linear space

From Wikipedia, the free encyclopedia

In mathematics a linear space can mean one of two things:

• In linear algebra or mathematical analysis, a vector space
• In geometry, an incidence structure of points and lines satisfying the following axioms:
  • There are at least two lines
  • Every line is incident with at least two points
  • The linear space axiom: for any given pair of points, there is exactly one line incident with both of these points.

If an incident structure satisfies the last two axioms, but only has one line, then it is called a degenerate linear space. Projective spaces and affine spaces are two important kinds of linear space.