A **diagonal matrix** has zero at every entry not on the diagonal. In a matrix $A=(a_{ij})$, it is *diagonal* if $a_{ij}=0\impliedby i\neq j$ Usually this name is only applied to a [[square matrix]] $ \left(\begin{array}{cccc}a_{1} & 0 & \cdots & 0 \\ 0 & a_{2} & \cdots & 0 \\ \vdots & \vdots & & \vdots \\ 0 & 0 & \cdots & a_{n}\end{array}\right) $ Special diagonal matrices: [[identity matrix]]