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Student[LinearAlgebra]

 BandMatrix
 construct a band Matrix

 Calling Sequence BandMatrix(L, n, options)

Parameters

 L - list of lists of scalars or list of scalars or Vector of scalars; diagonals of the band Matrix n - (optional) non-negative integer; the number of subdiagonals options - (optional) parameters; for a complete list, see LinearAlgebra[BandMatrix]

Description

 • 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 '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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $\mathrm{LL}≔\left[\left[w,w\right],\left[x,x,x\right],\left[y,y,y\right],\left[z,z\right]\right]:$
 > $\mathrm{BandMatrix}\left(\mathrm{LL}\right)$
 $\left[\begin{array}{ccc}{y}& {z}& {0}\\ {x}& {y}& {z}\\ {w}& {x}& {y}\\ {0}& {w}& {x}\end{array}\right]$ (1)
 > $\mathrm{BandMatrix}\left(\mathrm{LL},1\right)$
 $\left[\begin{array}{cccc}{x}& {y}& {z}& {0}\\ {w}& {x}& {y}& {z}\\ {0}& {w}& {x}& {y}\end{array}\right]$ (2)
 > $\mathrm{BandMatrix}\left(⟨1,2⟩,3\right)$
 $\left[\begin{array}{cccc}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {2}& {0}& {0}& {0}\\ {1}& {2}& {0}& {0}\end{array}\right]$ (3)

 See Also