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===Banded===
{{main article|Band matrix}}
A [[band matrix]] is a special class of sparse matrix where the non-zero elements are concentrated near the main diagonal. A band matrix is characterised by its lower and upper bandwidths, which refer to the number of diagonals below and above (respectively) the [[main diagonal]] between which all of the non-zero entries are contained.
An important special type of sparse matrices is [[band matrix]], defined as follows. The [[lower bandwidth of a matrix]] {{math|'''A'''}} is the smallest number {{math|''p''}} such that the entry {{math|''a''<sub>''i'',''j''</sub>}} vanishes whenever {{math|''i'' > ''j'' + ''p''}}. (The converse of this condition does not necessarily hold; there can be zero elements not satisfying this condition, but elements satisfying the condition are zero.) Similarly, the [[Band matrix#upper bandwidth|upper bandwidth]] is the smallest number {{math|''p''}} such that {{math|1=''a''<sub>''i'',''j''</sub> = 0}} whenever {{math|''i'' < ''j'' − ''p''}} {{harv|Golub|Van Loan|1996|loc=§1.2.1}}. For example, a [[tridiagonal matrix]] has lower bandwidth {{math|1}} and upper bandwidth {{math|1}}. As another example, the following sparse matrix has lower and upper bandwidth both equal to 3. Notice that zeros are represented with dots for clarity.▼
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<math display="block">\begin{bmatrix}
X & X & X & \cdot & \cdot & \cdot & \cdot & \\
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====Diagonal====
A
===Symmetric===
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