  Let $F$ be a graph. A hypergraph is called Berge $F$ if it can be obtained by
replacing each edge in $F$ by a hyperedge containing it. Given a family of
graphs $\mathcal{F}$, we say that a hypergraph $H$ is Berge $\mathcal{F}$-free
if for every $F \in \mathcal{F}$, the hypergraph $H$ does not contain a Berge
$F$ as a subhypergraph. In this paper we investigate the connections between
spectral radius of the adjacency tensor and structural properties of a linear
hypergraph. In particular, we obtain a spectral version of Tur\'{a}n-type
problems over linear $k$-uniform hypergraphs by using spectral methods,
including a tight result on Berge $C_4$-free linear $3$-uniform hypergraphs.
