Definition:Diagonal of Array/Main

Definition

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.

Also known as

The main diagonal of an array (such as a matrix or a determinant) is also known as:

the principal diagonal

the leading diagonal.

Also see

• Results about the main diagonal 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.