Definition:Diagonal of Determinant

Definition

Let $\mathbf D$ be a determinant.

A diagonal of $\mathbf D$ is a diagonal line of elements of $\mathbf D$.

Main Diagonal

Let $\mathbf D = \sqbrk d_{m n}$ be a determinant.

The elements $d_{j j}: j \in \closedint 1 {\min \set {m, n} }$ constitute the main diagonal of $\mathbf D$.

That is, the main diagonal is the diagonal of $\mathbf D$ from the top left corner, that is, the element $g_{1 1}$, running towards the lower right corner.

Main Antidiagonal

Let $\mathbf D = \sqbrk d_{m n}$ be a matrix.

The main antidiagonal of $\mathbf D$ is the antidiagonal of $\mathbf D$ from the top right corner, that is, the element $d_{1 n}$, running towards the lower left corner.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): determinant
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): determinant