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companion

companion matrix

Syntax

A=companion(p)

Arguments

p

polynomial or vector of polynomials

A

square matrix

Description

Returns a matrix A with characteristic polynomial equal to p if p is monic. If p is not monic the characteristic polynomial of A is equal to p/c where c is the coefficient of largest degree in p.

If p is a vector of monic polynomials, A is block diagonal, and the characteristic polynomial of the ith block is p(i).

Examples

s=poly(0,'s');
p=poly([1,2,3,4,1],'s','c')
det(s*eye(4,4)-companion(p))
roots(p)
spec(companion(p))

See also

  • spec — eigenvalues, and eigenvectors of a matrix or a pencil
  • poly — Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
  • randpencil — random pencil
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Last updated:
Mon Nov 07 14:58:52 CET 2022