# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Band

Band[{i,j}]
represents the sequence of positions on the diagonal band that starts with {i,j} in a sparse array.

Band[{imin,jmin,},{imax,jmax,}]
represents the positions between {imin,jmin,} and {imax,jmax,}.

Band[{imin,jmin,},{imax,jmax,},{di,dj,}]
represents positions starting with {imin,jmin,} and then moving with step {di,dj,}.

## DetailsDetails

• Band[pos]->v represents values v that repeat along the diagonal band starting at pos.
• Band[pos]->{v1,v2,} represents a sequence of values vn along the diagonal band starting at pos.
• With an array a of the same rank as the whole sparse array, Band[start]->a by default inserts a at the position specified by start.
• With arrays an of the same rank as the whole sparse array, Band[pos]->{a1,a2,} represents a sequence of non-overlapping subarrays.
• Band[start] is effectively equivalent to Band[start,{-1,-1,}].
• For scalar values, Band[start,end] is equivalent to Band[start,end,{1,1,}].
• Band[start,end,step] stops when any coordinate first exceeds its value in end.
• Band[start,end]->{v1,v2,} takes the values vn to repeat cyclically until end is reached.
• Band[start,Automatic,step]->a continues until the edge of the array is reached.
• Band[start,Automatic,step]->{v1,v2,} continues until the vi are exhausted.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

Create a band diagonal matrix:

 In[1]:=
 Out[1]//MatrixForm=

Convert to normal lists:

 In[2]:=
 Out[2]=