Editing Diagonal matrix (section)

{{Use American English|date = March 2019}}
{{Short description|Matrix whose only nonzero elements are on its main diagonal}}

In [[linear algebra]], a '''diagonal matrix''' is a [[matrix (mathematics)|matrix]] in which the entries outside the [[main diagonal]] are all zero; the term usually refers to [[square matrices]]. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is <math>\left[\begin{smallmatrix}
3 & 0 \\
0 & 2 \end{smallmatrix}\right]</math>, while an example of a 3×3 diagonal matrix is<math>
\left[\begin{smallmatrix}
6 & 0 & 0 \\
0 & 5 & 0 \\
0 & 0 & 4
\end{smallmatrix}\right]</math>. An [[identity matrix]] of any size, or any multiple of it is a diagonal matrix called a [[#Scalar matrix|''scalar matrix'']], for example, <math>\left[\begin{smallmatrix}
0.5 & 0 \\
0 & 0.5 \end{smallmatrix}\right]</math>. 
In [[geometry]], a diagonal matrix may be used as a ''[[scaling matrix]]'', since matrix multiplication with it results in changing scale (size) and possibly also [[shape]]; only a scalar matrix results in uniform change in scale.