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G. Eric Moorhouse is a mathematician whose work includes finite geometry, incidence structures and coding theory. His author homepage identifies him as Eric Moorhouse and records a University of Wyoming faculty appointment beginning in 1989.^[ref]

With Aart Blokhuis, he computed characteristic-$p$ rank formulas for the point-hyperplane incidence matrix of a set system in finite orthogonal geometries. Their calculations yield bounds on ovoids and rule out their existence in several families.^[ref] The link is that an incidence matrix converts containment statements into vectors over a finite field. A proposed geometric configuration must satisfy the resulting linear constraints, so linear algebra can prove that the configuration cannot exist. This makes incidence ranks useful structural information, rather than merely a numerical summary of a matrix.

In the point-block convention, an incidence structure consists of a set $P$ of points, a set $B$ of blocks, and a relation $I\subseteq P\times B$ specifying which points lie on which blocks. Blocks are abstract objects: distinct blocks may have identical sets of incident points unless a simplicity condition forbids this. A finite incidence structure is encoded by its incidence matrix of a set system, with entry $1$ for incidence and $0$ otherwise.

For example, take points $1,2,3$ and three blocks incident with $\{1,2\}$, $\{2,3\}$ and $\{1,3\}$. With points indexing rows, the incidence matrix of a set system isEvery point lies on two blocks, every block contains two points, and every pair of distinct points lies on exactly one block. It is a $2$-$(3,2,1)$ combinatorial design. Its matrix rank is three over $\mathbb{Q}$ but two over ${\mathbb{F}}_2$, since its determinant is two. This illustrates why incidence and the coefficient field jointly matter in algebraic counting arguments.

Finite geometries, graphs and combinatorial designs all supply incidence structures, but additional axioms distinguish their particular classes. Merely specifying incidence does not require any balanced-design or projective-plane axioms. Typed incidence structures can include further element types, such as points, lines and planes.^[ref]