The characteristic polynomial of a square matrix A is the
polynomial
P(x)=det(xI−A)
The charpoly command finds the characteristic polynomial of a
matrix. pcar is a synonym for charpoly.
charpoly takes one mandatory argument and one
optional argument:
A, a square matrix.
Optionally, x, a variable name.
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.
Examples.
Input:
charpoly([[4,1,-2],[1,2,-1],[2,1,0]])
Output:
⎡
⎣
1,−6,12,−8
⎤
⎦
Hence, the characteristic polynomial of this matrix is
x3−6x2+12x−8.