= Solution
The <minimal polynomial> of a <linear transformation> $T$ is the unique <monic polynomial> of least <degree> among the nonzero <polynomials> $p\in F[x]$ satisfying $p(T)=0$:
$$
\boxed{m_T\text{ monic},\quad m_T(T)=0,\quad\deg m_T\text{ least possible}.}
$$
Such a <polynomial> exists because the <endomorphism> space is finite-dimensional, so sufficiently many <powers> $I,T,T^2,\ldots$ are <linearly dependent>. Monic normalization is possible over the <field> $F$. Two <monic polynomials> annihilating $T$ of the same least <degree> have a difference of smaller <degree> annihilating $T$, so their difference is zero. For the zero <vector space> the convention is $m_T=1$.
Back to article page
