minpoly

Compute Minimal Polynomial of Matrix

Compute the minimal polynomial of the matrix A in terms of the variable x:

syms x
A = sym([1 1 0; 0 1 0; 0 0 1]);
minpoly(A, x)

ans =
x^2 - 2*x + 1

Compute Coefficients of Minimal Polynomial

To find the coefficients of the minimal polynomial of A, call minpoly with one argument. Since A is numeric, minpoly returns coefficients as double-precision values:

A = sym([1 1 0; 0 1 0; 0 0 1]);
minpoly(A)

ans =
[ 1, -2, 1]

Find the coefficients of the minimal polynomial of the symbolic matrix A. For this matrix, minpoly returns the symbolic vector of coefficients:

A = sym([0 2 0; 0 0 2; 2 0 0]);
P = minpoly(A)

P =
[ 1, 0, 0, -8]