Diagonal matrix: Difference between revisions

Revision as of 03:33, 23 November 2023

Revision as of 03:34, 23 November 2023

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{{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 fvdvdisis <math>\left[\begin{smallmatrix}

3 & 0 \\

0 & 2 \end{smallmatrix}\right]</math>, while an example of a 3×3 diagonal matrix is<math>

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0.5 & 0 \\

0 & 0.5 \end{smallmatrix}\right]</math>.

In [[geometry]], vgf 6jaa 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.

==Definition==