Definition:Diagonal
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Diagonal may refer to:
- 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.