Incidence matrix of a set system
= Incidence matrix of a set system
{title2=$B_{i,j}=\mathbf1_{i\in A_j}$}
For a finite ground <set> and an indexed <set family>, this zero-one <matrix> records membership of points in members. The diagonal entries of $B^TB$ are member sizes, and its off-diagonal entries count pairwise <intersections>. For the <Fano plane>, either point-line orientation gives the identity $B^TB=2I+J$, since every point lies on three lines and each distinct point pair lies on one line.