Definition:Matrix/Diagonal/Main
< Definition:Matrix | Diagonal(Redirected from Definition:Main Diagonal)
Jump to navigation
Jump to search
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 elements 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