### 5.48.8 Minimal polynomial : pmin

pmin takes one (resp. two) argument(s):
a square matrix A of size n and optionally
the name of a symbolic variable.

pmin returns the minimal polynomial of A written as a
list of its coefficients if no variable was provided, or
written in symbolic form with respect to the
variable name given as second argument.
The minimal polynomial of A is the polynomial P
having minimal degree such that P(A)=0.

Input :

pmin([[1,0],[0,1]])

Output :

[1,-1]

Input :

pmin([[1,0],[0,1]],x)

Output :

x-1

Hence the minimal polynomial of [[1,0],[0,1]] is x-1.

Input :

pmin([[2,1,0],[0,2,0],[0,0,2]])

Output :

[1,-4,4]

Input :

pmin([[2,1,0],[0,2,0],[0,0,2]],x)

Output :

x`^`

2-4*x+4

Hence, the minimal polynomial of [[2,1,0],[0,2,0],[0,0,2]] is x^{2}−4x+4.