Editing Band matrix (section)

===Bandwidth===

Formally, consider an ''n''&times;''n'' matrix ''A''=(''a''<sub>''i,j'' </sub>). If all matrix elements are zero outside a diagonally bordered band whose range is determined by constants ''k''<sub>1</sub> and ''k''<sub>2</sub>:

:<math>a_{i,j}=0 \quad\mbox{if}\quad j<i-k_1 \quad\mbox{ or }\quad j>i+k_2; \quad k_1, k_2 \ge 0.\,</math>

then the quantities ''k''<sub>1</sub> and ''k''<sub>2</sub> are called the '''{{visible anchor|lower bandwidth}}''' and '''{{visible anchor|upper bandwidth}}''', respectively.{{sfn|Golub|Van Loan|1996|loc=§1.2.1}} The '''{{visible anchor|bandwidth}}''' of the matrix is the maximum of ''k''<sub>1</sub> and ''k''<sub>2</sub>; in other words, it is the number ''k'' such that <math> a_{i,j}=0 </math> if <math> |i-j| > k </math>.{{sfn|Atkinson|1989|p=527}}