  Let $k$ be a field and $A\in M_n(k)$ be an $n\times n$ matrix. We denote
$C_{M_n(k)}(A) = \{B\in M_n(k) : BA = AB\}$ be its centralizers in $M_n(k)$.
The dimension of the space of centralizer was already known by Frobenius. This
paper will give the explicit $k$-basis for $C_{M_n(k)}(A)$ and also an
algorithm (with polynomial complexity respect to multiplication in the field
$k$) to construct the explicit basis. Lastly, the result can be used to solve a
weaker version of the Wild Problem.
