Definition:Array/Diagonal

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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