Definition:Array/Diagonal
Definition
Let $\mathbf A = \sqbrk a_{m n}$ be an array.
The diagonals are the lines of elements of $\mathbf A$ running from:
- $(1): \quad$ the element in the first row and first column running downwards and to the right
- $(2): \quad$ the element in the first row and last column running downwards and to the left
- $(3): \quad$ the element in the last row and first column running upwards and to the right
- $(4): \quad$ the element in the last row and last column running upwards and to the left
If $m = n$, that is, if $\mathbf A$ is a square array, then $(1)$ and $(4)$ coincide, and $(2)$ and $(3)$ also coincide.
Main Diagonal
Let $\mathbf A = \sqbrk a_{m n}$ be an array.
The elements $a_{j j}: j \in \closedint 1 {\min \set {m, n} }$ constitute the main diagonal of $\mathbf A$.
That is, the main diagonal is the diagonal of $\mathbf A$ from the top left corner, that is, the element $a_{1 1}$, running towards the lower right corner.
Main Antidiagonal
Let $\mathbf A = \sqbrk a_{m n}$ be an array.
The main antidiagonal of $\mathbf A$ is the antidiagonal of $\mathbf A$ from the top right corner, that is, the element $a_{1 n}$, running towards the lower left corner.
Also defined as
Some sources define the diagonals of an array only for a square array.
Also see
- Results about diagonals of arrays can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): diagonal: 3.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): diagonal: 3.