Method on @sym: charpoly (A) ¶

Method on @sym: charpoly (A, x) ¶

Characteristic polynomial of symbolic matrix.

Numerical example:

A = sym([1 2; 3 4]);
mu = sym('mu');
charpoly (A, mu)
  ⇒ (sym)
       2
      μ  - 5⋅μ - 2

We can then manipulate the characteristic polynomial, for example:

b(mu) = charpoly (A, mu)
  ⇒ b(mu) = (symfun)
       2
      μ  - 5⋅μ - 2
b(1)
  ⇒ (sym) -6

We can also confirm that the characteristic polynomial is zero at an eigenvalue:

ev = eig(A);
simplify(b(ev(1)))
  ⇒ (sym) 0

The matrix can contain symbols:

syms x
charpoly ([x x;1 x], sym('lambda'))
  ⇒ (sym)
       2            2
      λ  - 2⋅λ⋅x + x  - x

If x is omitted, the polynomial coefficients are returned:

charpoly (sym([4 1;3 9]))
  ⇒ ans = (sym) [1  -13  33]  (1×3 matrix)

See also: @@sym/eig, @@sym/jordan.

Package: symbolic