Quiver representation space
= Quiver representation space
{title2=$\operatorname{Rep}_Q(\mathbf n)$}
= Representation space of a quiver
{synonym}
At fixed dimension vector, $\operatorname{Rep}_Q(\mathbf n)=\prod_{\rho:i\to j}\operatorname{Hom}_k(k^{n_i},k^{n_j})$ is an irreducible <affine space> of dimension $\sum_\rho n_{s(\rho)}n_{t(\rho)}$. Its points are arrow-matrix collections, and its base-change orbits are isomorphism classes.