# Diagonal

## Meanings and phrases

adj.

- connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face
- having an oblique or slanted direction; aslant; aslope; slanted; slanting; sloped; sloping

n.

- (geometry) a straight line connecting any two vertices of a polygon that are not adjacent
- a line or cut across a fabric that is not at right angles to a side of the fabric; bias
- an oblique line of squares of the same color on a checkerboard
- (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry
- a punctuation mark (/) used to separate related items of information; solidus; slash; virgule; stroke; separatrix

n.

- a square matrix with all elements not on the main diagonal equal to zero

- If all entries outside the main diagonal are zero, A is called a diagonal matrix.
- (It is represented in any coordinate system by a 3 × 3 diagonal matrix with equal values along the diagonal.)
- Singular value decomposition expresses any matrix A as a product UDV, where U and V are unitary matrices and D is a diagonal matrix.

n.

- the diagonal of a square matrix running from the upper left entry to the lower right entry; principal diagonal

n.

- the diagonal of a square matrix running from the upper left entry to the lower right entry; main diagonal

n.

- the diagonal of a square matrix running from the lower left entry to the upper right entry

E.g.

- The outer facing corners have diagonal buttresses.
- The two-stage west tower is supported by diagonal buttresses.
- The chancel has diagonal buttresses on the north-east and south-east corners.