Campus Livre
compan
Companion matrix of a polynomial.
Category: Mathematics > Elementary Math
Syntax
A = compan(u)Returns the companion matrix of the polynomial whose coefficients are in u.
Description
The first row of A is -u(2:end) / u(1) and the subdiagonal holds ones. The eigenvalues of A are the roots of the polynomial, which is how roots finds them. For u = [1 2 3] the result is [-2 -3; 1 0].
Input arguments
u- Vector of polynomial coefficients, highest power first. The first entry must be nonzero.
Output arguments
A- Square matrix of size
numel(u) - 1.
Example
Roots through eigenvalues
u = [1 -3 2];
A = compan(u)
eig(A)Output
A = 2×2
3 -2
1 0
ans = 2×1
1.0000
2.0000