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# Definition of the (main) diagonal of a matrix

Put content here**Definition:** The **main diagonal** (or simply **diagonal**) of a matrix $A = (a_{ij})$ is the set of entries $a_{ii}$ where the row and column indices are equal:
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$$\text{diag}(A) = \{a_{11}, a_{22}, a_{33}, \ldots\}$$
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For an $m \times n$ matrix, the main diagonal consists of entries where $i = j$, running from the upper-left corner to the lower-right corner.
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**Example:** For
$$A = \begin{pmatrix} \mathbf{1} & 2 & 3 \\ 4 & \mathbf{5} & 6 \\ 7 & 8 & \mathbf{9} \end{pmatrix}$$
the main diagonal entries are $1, 5, 9$.
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The **trace** of a square matrix is the sum of its diagonal entries: $\text{tr}(A) = \sum_i a_{ii}$.

# Parents

* Basic terminology and notation