### 2.46.6 Characteristic polynomial : `charpoly`

`charpoly` (or `pcar`) takes one or two argument(s),
a square matrix *A* of size *n* and optionnally
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

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}−6*x*^{2}+12*x*−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`