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===Banded===
{{main article|Band matrix}}
An important special type of sparse matrices is a [[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''}}. 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.
<math display="block">\begin{bmatrix}
X & X & X & \cdot & \cdot & \cdot & \cdot & \\
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