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Student[LinearAlgebra]

  

BandMatrix

  

construct a band Matrix

 

Calling Sequence

Parameters

Description

Examples

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+1st 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: Lnj+1 is placed in the jth subdiagonal for j=1..n and Ln+k+1 is placed in the kth superdiagonal for k=1..nopsLn1. 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=iquonopsL,2 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

withStudent[LinearAlgebra]:

LLw,w,x,x,x,y,y,y,z,z:

BandMatrixLL

yz0xyzwxy0wx

(1)

BandMatrixLL,1

xyz0wxyz0wxy

(2)

BandMatrix1,2,3

0000000020001200

(3)

See Also

LinearAlgebra[BandMatrix]

Student[LinearAlgebra]

 


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