Let $k$ be a field, $V$ a vector space over $k$ and $T\colon V\to V$ a linear operator. We say that a subspace $W$ of $V$ is $T$ admissible if

1. $W$ is a $T$ - invariant subspace;
2. If $f \in k[X]$ (See the polynomial ring definition) and $f(T)x \in W$ there is a vector $y \in W$ such that $f(T)x=f(T)y$