The BandMatrix(L) command constructs a band Matrix from the data provided by L.

If L is a list of lists, then each list element in L is used to initialize a diagonal. The $n+1$st element of L is placed along the main diagonal. (If L has fewer than n+1 elements, it is automatically extended by [0]'s.)  The other diagonals are placed in relation to it: $L_{n-j+1}$ is placed in the jth subdiagonal for $j=1..n$ and $L_{n+k+1}$ is placed in the kth superdiagonal for $k=1..\mathrm{nops}\left(L\right)-n-1$. If any list element is shorter than the length of the diagonal where it is placed, the remaining entries are filled with 0.

If n is omitted  in the calling sequence, BandMatrix attempts to place an equal number of sub- and super-diagonals into the resulting Matrix by using $n=\mathrm{iquo}\left(\mathrm{nops}\left(L\right)\,2\right)$ subdiagonals.

If L is a list or Vector of scalars, its elements are used to initialize all the entries of the corresponding diagonals. In this case, parameter n must be specified in the calling sequence. If the row dimension r is not specified, it defaults to n+1.  If the column dimension is not specified, it defaults to the row dimension. The jth subdiagonal is filled with L[n-j+1] for j = 1 .. n. (If L has fewer than n+1 elements, it is automatically 0-extended.)  The main diagonal is filled with L[n + 1]. The kth superdiagonal is filled with L[n + k + 1] for k = 1 .. nops(L)- n - 1.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$\mathrm{LL}≔\left[\left[w\,w\right]\,\left[x\,x\,x\right]\,\left[y\,y\,y\right]\,\left[z\,z\right]\right]\:$

$\mathrm{BandMatrix}\left(\mathrm{LL}\right)$

$\left[\begin{array}{ccc}y& z& 0\\ x& y& z\\ w& x& y\\ 0& w& x\end{array}\right]$

$\mathrm{BandMatrix}\left(\mathrm{LL}\,1\right)$

$\left[\begin{array}{cccc}x& y& z& 0\\ w& x& y& z\\ 0& w& x& y\end{array}\right]$

$\mathrm{BandMatrix}\left(⟨1\,2⟩\,3\right)$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 2& 0& 0& 0\\ 1& 2& 0& 0\end{array}\right]$