Today I came across this notation:
Let $V$ be a vector space over the field $\mathbb{F}$, let $\phi:V\to V$ be a linear map and $\alpha\in \mathbb{F}$. Show that (some property) holds for $V(\alpha, \phi)$.
I have never come across the notation $V(\alpha,\phi)$ so far but my guess is that it has something to do with the image.