Diagonal Matrix

linear-algebra

Definition

Diagonal Matrix

A diagonal matrix $D=\mathrm{diag}({\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n)$ is a matrix where each element $D_{ii}$ is equal to ${\lambda }_i$:

$$D=\mathrm{diag}({\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n)=\left[\begin{array}{cccc}{\lambda }_1& 0& \dots & 0\\ 0& {\lambda }_2& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & {\lambda }_n\end{array}\right]$$