Characteristic polynomial

The characteristic polynomial of a square matrix A is the polynomial

P(x)=det(x I−A).

The charpoly or pcar command finds the characteristic polynomial of a matrix.

charpoly takes one mandatory argument and one or two optional argument(s):
- A, a square matrix.
- Optionally, x, a variable name.
- Optionally, fadeev, the symbol.
charpoly(A ⟨,x⟩) returns the characteristic polynomial of A. It is written as the list of its coefficients if no variable name was provided or written as an expression with respect to x if there is a second argument. If the last argument is fadeev, then charpoly will use the Faddeev–LeVerrier algorithm.

charpoly([[4,1,-2],[1,2,-1],[2,1,0]])

⎡
⎣

1,−6,12,−8

⎤
⎦

Hence, the characteristic polynomial of this matrix is x³−6x²+12x−8.

charpoly([[4,1,-2],[1,2,-1],[2,1,0]],X)

X³−6 X²+12 X−8