A [[Matrix]] is Diagonal if the only non-zero elements are located in the diagonal of the matrix.
$\huge
\forall ij : A_{ij} \neq 0 \iff i=j
$
A diagonal [[Matrix]] can be thought of as a [[Resize Transformation]] around the [[Standard Basis]].
>[!example] Visualization
>![[../../00 Excalidraw/Diagonal Matrix _0.excalidraw.dark.svg]]
>%%[[../../00 Excalidraw/Diagonal Matrix _0.excalidraw.md|🖋 Edit in Excalidraw]], and the [[../../00 Excalidraw/Diagonal Matrix _0.excalidraw.light.svg|light exported image]]%%