I am reading this page to try to understand Jordan form. $V$ is a finite-dimensional complex vector space, and until now $T$ has always represented an "operator", by which I guess they mean a linear transformation.
Towards the bottom of the first page they write $(T - \lambda I)v= 0$. Now I know that with any linear transformation $T:V \to V$ we can associate a matrix. However, that matrix is usually represented as $[T]_{B \leftarrow B}$.
Is $([T]_{B \leftarrow B} - \lambda I) [v]_B$ what they probably meant to write on the website, or does $(T - \lambda I)v$ have a meaning somehow when $T$ is just a linear transformation?