@sym
: charpoly (A) ¶@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