The Hessenberg Indexing Function - Maple Help

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The Hessenberg Indexing Function

Description

• 

The Hessenberg indexing function can be used to construct rtable objects of type Array or Matrix.

• 

In the construction of a Matrix, if Hessenberg or Hessenberg[upper] is included in the calling sequence as an indexing function (shape), an upper Hessenberg Matrix is returned.

  

Note:  A Hessenberg Matrix is a triangular Matrix with one extra (contiguous) diagonal.

• 

This indexing function may also be qualified as Hessenberg[lower].

• 

The specification is similar in the construction of an Array.

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If an object is defined by using the Hessenberg or Hessenberg[upper] indexing function, the elements located in the lower triangle, below the subdiagonal, cannot be reassigned.

  

The situation is similar in a construction that uses Hessenberg[lower] as an indexing function.

Examples

A:=ArrayHessenbergupper,1..4,1..4,a,b→a+b

A:=2345345605670078

(1)

M:=Matrix3,1,1,1,1,1,1,1,1,1,shape=Hessenberglower

M:=110111111

(2)

M1,2:=5

M1,2:=5

(3)

M

150111111

(4)

M1,3:=5

Error, attempt to assign to upper triangle of lower Hessenberg rtable

See Also

Array, Matrix, rtable, rtable_indexfcn


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