compan - Companion matrix

Syntax

Description

A = compan(u) returns the corresponding companion matrix whose first row is -u(2:n)/u(1), where u is a vector of polynomial coefficients. The eigenvalues of compan(u) are the roots of the polynomial.

Examples

The polynomial (x – 1)(x – 2)(x + 3) = x³ – 7x + 6 has a companion matrix given by

u = [1  0  -7  6]
A = compan(u)
A =
    0    7   -6
    1    0    0
    0    1    0

The eigenvalues are the polynomial roots:

eig(compan(u))

ans = 
    -3.0000
     2.0000
     1.0000

This is also roots(u).

See Also

eig | poly | polyval | roots

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