# Linear Algebra/Diagonal Matrix

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A diagonal matrix, ${\displaystyle A}$, is a square matrix in which the entries outside of the main diagonal are zero. The main diagonal of a square matrix consists of the entries which run from the top left corner to the bottom right corner.

In the example below the main diagonal are ${\displaystyle a_{11},a_{22},...,a_{nn}\!}$

${\displaystyle \quad A={\begin{bmatrix}a_{11}&0&\cdots &0\\0&a_{22}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &a_{nn}\end{bmatrix}}}$