  An $r$-uniform hypergraph is linear if every two edges intersect in at most
one vertex. The $r$-expansion $F^{r}$ of a graph $F$ is the $r$-uniform
hypergraph obtained from $F$ by enlarging each edge of $F$ with a vertex subset
of size $r-2$ disjoint from the vertex set of $F$ such that distinct edges are
enlarged by disjoint subsets. Let $ex_{r}^{lin}(n,F^{r})$ and
$spex_{r}^{lin}(n,F^{r})$ be the maximum number of edges and the maximum
spectral radius of all $F^{r}$-free linear $r$-uniform hypergraphs with $n$
vertices, respectively. In this paper, we present the sharp (or asymptotic)
bounds of $ex_{r}^{lin}( n,F^{r})$ and $spex_{r}^{lin}(n,F^{r})$ by
establishing the connection between the spectral radii of linear hypergraphs
and those of their shadow graphs, where $F$ is a $(k+1)$-color critical graph
or a graph with chromatic number $k$.
