  Let $K$ be a simplical complex, and let $\mathcal{L}_i^{up}(K),
\mathcal{Q}_i^{up}(K)$ be the $i$-th up Laplacian and signless Laplacian of
$K$, respectively. In this paper we proved that the largest eigenvalue of
$\mathcal{L}_i^{up}(K)$ is not greater than the largest eigenvalue of
$\mathcal{Q}_i^{up}(K)$; furthermore, if $K$ is $(i+1)$-path connected, then
the equality holds if and only if the $i$-th incidence signed graph $B_i(K)$ of
$K$ is balanced. As an application we provided an upper bound for the largest
eigenvalue of the $i$-th up Laplacian of $K$, which improves the bound given by
Horak and Jost and generalizes the result of Anderson and Morley on graphs.We
characterized the balancedness of simplicial complexes under operations such as
wedge sum, join, Cartesian product and duplication of motifs. For each $i \ge
0$, by using wedge sum or duplication of motifs, we can construct an infinitely
many $(i+1)$-path connected simplicial complexes $K$ with $B_i(K)$ being
balanced.
