charpoly (or pcar) takes one or two argument(s),
a square matrix A of size n and optionally
the name of a symbolic variable.

charpoly returns the characteristic polynomial
P of A written as the
list of its coefficients if no variable name was provided
or written as an expression with respect to
the variable name provided as second argument.

The characteristic polynomial P of A is defined as

P(x)=det(x I−A) |

Input :

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

Output :

[1,-6,12,-8]

Hence, the characteristic polynomial of this matrix is
x^{3}−6x^{2}+12x−8 (input normal(poly2symb([1,-6,12,-8],x)) to get
its symbolic representation).

Input :

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

Output :

X

`^`

3-6*X`^`

2+12*X-8