Definition:Diagonal


 * Geometry:
 * Another name for the diameter of a quadrilateral.


 * Relation Theory:
 * The diagonal relation on a set $S$ is the relation $\Delta_S \subseteq S \times S$ defined as: $\left\{{\left({x, x}\right): x \in S}\right\}$.


 * Mapping Theory:
 * The diagonal mapping on a set $S$ is the mapping $\Delta$ from $S$ to $S \times S$ defined as: $\forall x \in S: \Delta \left({x}\right) = \left({x, x}\right)$.


 * Matrix Algebra:
 * The diagonal elements of a square matrix $\mathbf A = \left[{a}\right]_n$ are the matrix elements $a_{j j}: j \in \left[{1 \,.\,.\, n}\right]$.
 * Diagonal matrix: a square matrix whose only non-zero matrix elements are diagonal elements.