Definition:Matrix/Diagonal Elements
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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 the matrix.
The elements themselves are called the diagonal elements.
Also defined as
Some sources define the diagonal elements only for a square matrix.
Also known as
Some sources refer to diagonal entries.
The main diagonal is also known as the principal diagonal and the leading diagonal.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.2$: Functions on vectors: $\S 2.2.3$: $m \times n$ matrices
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): main diagonal, main antidiagonal
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): diagonal entry
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): leading diagonal
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): main diagonal