companion

Arguments

p

double or polynomial vector

A

square matrix

Description

A = companion(p) with p which is a vector of polynomial coefficients returns the companion matrix. The coefficients must be in order of decreasing degree.

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

Companion matrix created from a polynom

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

Companion matrix created from vector of polynomial coefficients

// p = x4 + 4x3 + 3x2 + 2x + 1
c = [1 4 3 2 1];
companion(c)

See also

• spec — 行列とペンシルの固有値
• poly — Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
• randpencil — ランダムなペンシル

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