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linalg(deprecated)

  

companion

  

companion matrix associated with a polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

companion(p, x)

Parameters

p

-

monic univariate polynomial in x

x

-

name (the variable)

Description

• 

Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[CompanionMatrix], instead.

  

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

• 

The call companion(p, x) will return a companion matrix associated with the polynomial p(x).

• 

If C := companion(p, x) and p is a0+a1x+...+xn (a monic univariate polynomial) then Ci,n=coeffp,x,i1 (i=1..n), Ci,i1=1 (i=2..n), and Ci,j=0 for other values of i and j.

• 

The command with(linalg,companion) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[CompanionMatrix], instead.

withlinalg:

px4+9x3+2x2+17x+5

px4+9x3+2x2+17x+5

(1)

companionp,x

00051001701020019

(2)

qexpandz+2z5z+3

qz319z30

(3)

companionq,z

00301019010

(4)

See Also

linalg(deprecated)[diag]

linalg(deprecated)[JordanBlock]

LinearAlgebra