Analytical Study of Seven-Dimensional Projective Space

Abstract

Analytical studies of finite projective spaces of interest make understanding space objects much easier. In this paper, an analytic study is given of the finite projective space of dimension seven. Formulas of some combinatorial properties and details are found like, number of i-spaces through j-spaces, i>j, spaces resulting from the intersection of two spaces, i-space with j-space i≠j, and the relation between lines and skew lines. Also, the basic conditions to spread the space by lines were also found. All obtained results were implemented on the finite projective space of dimension seven over the finite field of order two as an example.