TITLE: Calculate minimal polynomial of a matrix
QUESTION [8 upvotes]: \begin{bmatrix}0&1&0&1\\1&0&1&0\\0&1&0&1\\1&0&1&0\end{bmatrix}
I have calculated characteristic polynomial as $x^2(x^2-4)$ but I don't know what is minimal polynomial please solve

REPLY [8 votes]: As the given matrix is symmetric it is diagonalizable $\Rightarrow$ its minimal polynomial has distinct roots  $\Rightarrow$ minimal polynomial $= x(x-2)(x+2)$.