Definition:Matrix/Diagonal/Main

Definition

Let $\mathbf A = \sqbrk a_{m n}$ be a matrix.

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 of $\mathbf A$ is the diagonal of $\mathbf A$ from the top left corner, that is, the element $a_{1 1}$, running towards the lower right corner.

Diagonal Elements

The element of the main diagonal of a matrix or a determinant are called the diagonal elements.

Also defined as

Some sources define the main diagonal only for a square matrix.

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

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): matrix (plural matrices)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): main diagonal, main antidiagonal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): matrix (plural matrices)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): main diagonal