Incidence relation

Incidence is a relation between geometric subspaces (points, lines, planes, &c.), generalizing the notion of a point being on a line, a line being in a plane, a plane containing a line, &c. In each case the subspaces are said to be incident with one another.

Incidence matrix

Given subspaces $(𝑝 𝑖) 𝑛 𝑖 = 1$ of one type and subspaces $(ℓ 𝑖) 𝑚 𝑖 = 1$ of another, the incidence relationship between these may be summarized by an $𝑚 \times 𝑛$ incidence matrix #m/def/geo

[I] = ⎡ ⎢ ⎢ ⎣ [ℓ 1 I 𝑝 1] \dots [ℓ 1 I 𝑝 𝑛] ⋮ ⋱ ⋮ [ℓ 𝑚 I 𝑝 1] \dots [ℓ 𝑚 I 𝑝 𝑛] ⎤ ⎥ ⎥ ⎦ \in M 𝑚 \times 𝑛 (𝕂 2)

where we have invoked the Iverson bracket.

#state/tidy | #lang/en | #SemBr