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By rearranging the rows and columns of a matrix {{math|'''A'''}} it may be possible to obtain a matrix {{math|'''A'''′}} with a lower bandwidth. A number of algorithms are designed for [[Graph bandwidth|bandwidth minimization]].
====Diagonal====
A very efficient structure for an extreme case of band matrices, the ''[[diagonal matrix]]'', is to store just the entries in the [[main diagonal]] as a [[one-dimensional array]], so a diagonal {{math|''n'' × ''n''}} matrix requires only {{math|''n''}} entries.
===Symmetric===
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