Definition:Diagonal


 * Geometry:
 * Another name for the chord of a polygon.
 * Diagonal of a polyhedron
 * Another name for the diameter of a quadrilateral.
 * Diagonal of a parallelogram


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


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


 * Matrix Algebra:
 * The diagonal elements of a square matrix $\mathbf A = \sqbrk a_n$ are the matrix elements $a_{j j}: j \in \closedint 1 n$.
 * Diagonal matrix: a square matrix whose only non-zero matrix elements are diagonal elements.

Also see

 * Definition:Diagonalizable