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Student[LinearAlgebra]

  

CompanionMatrix

  

construct the companion Matrix of a monic polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CompanionMatrix(P, options)

Parameters

P

-

monic polynomial

options

-

(optional) parameters; for a complete list, see LinearAlgebra[CompanionMatrix]

Description

• 

The CompanionMatrix(P) command returns the companion Matrix associated with the univariate polynomial Px.

• 

If C := CompanionMatrix(P) and P is a0+a1x+...+xn (a monic univariate polynomial), then  C is an nxn Matrix where n is the degree of polynomial P, Ci,n=coeffP,x,i1i=1..n, Ci,i1=1i=2..n, and Ci,j=0 for all other values of i and j.

Examples

withStudent[LinearAlgebra]:

px4+x3+2x2+3x

p:=x4+x3+2x2+3x

(1)

CompanionMatrixp

0000100301020011

(2)

qz+2z5z+3

q:=z+2z5z+3

(3)

CompanionMatrixq

00301019010

(4)

See Also

coeff

LinearAlgebra[CompanionMatrix]

Student[LinearAlgebra]

Student[LinearAlgebra][CharacteristicPolynomial]

 


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