Main diagonal

Definition

The main diagonal or principal diagonal of a square matrix is defined as the set of positions (and corresponding entries) in the matrix where the row and column index are equal. Explicitly, suppose $n$ is a natural number and $A=(a_{ij})_{1\leq i\leq n,1\leq j\leq n}$ is a $n\times n$ square matrix. The main diagonal of $A$ is the collection of entries:

$\{a_{ii}:1\leq i\leq n\}$

In cases where there is no ambiguity, the main diagonal is simply referred to as the diagonal.