2-Ranks of incidence matrices associated with conics in finite projective planes

In this article, we investigate geometric properties of the secant-internal neighbors of internal points and the passant-external neighbors of external points in classical finite projective planes; we calculate the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-ranks of the incidence matrices of internal points versus their secant-internal neighbors and external points versus their passant-external neighbors using a combination of techniques from both finite geometry and linear algebra.