compute the Hessenberg form of a square Matrix - Maple Help

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LinearAlgebra[Generic][HessenbergForm] - compute the Hessenberg form of a square Matrix

Calling Sequence

HessenbergForm[F](A)

HessenbergForm[F](A,output=out)

Parameters

F

-

a table or module, the domain of computation, a field

A

-

square Matrix of values in F

out

-

one of H, U or a list containing one or more of these names

Description

• 

HessenbergForm[F](A) returns the upper Hessenberg form H of A.

• 

Given an n x n Matrix A of elements in a field F, the algorithm converts a copy of A into upper Hessenberg form H using O(n^3) operations in F. The algorithm requires that F be a field and should only be used if F is finite as there is severe expression swell in computing H.

• 

The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:

  

F[`0`]: a constant for the zero of the ring F

  

F[`1`]: a constant for the (multiplicative) identity of F

  

F[`+`]: a procedure for adding elements of F (nary)

  

F[`-`]: a procedure for negating and subtracting elements of F (unary and binary)

  

F[`*`]: a procedure for multiplying two elements of F (commutative)

  

F[`/`]: a procedure for dividing two elements of F

  

F[`=`]: a boolean procedure for testing if two elements in F are equal

Examples

withLinearAlgebra[Generic]:

Q`0`,Q`1`,Q`+`,Q`-`,Q`*`,Q`/`,Q`=`:=0,1,`+`,`-`,`*`,`/`,`=`:

A:=Matrix2,7,3,4,1,3,4,5,7,10,5,7,7,10,5,7

A:=273413457105771057

(1)

H:=HessenbergFormQA

H:=21414110150465280000

(2)

H,U:=HessenbergFormQA,output='H','U'

H,U:=21414110150465280000,1000010007100011

(3)

MatrixMatrixMultiplyQMatrixMatrixMultiplyQU,A,MatrixInverseQU

21414110150465280000

(4)

See Also

Hessenberg Form , LinearAlgebra[Generic], LinearAlgebra[Generic][HessenbergAlgorithm], LinearAlgebra[Generic][MatrixMatrixMultiply], LinearAlgebra[HessenbergForm]


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