A signing of a graph $G=(V,E)$ is a function $s:E \rightarrow \{-1,1\}$. A signing defines a graph $\widehat{G}$, called a {\em 2-lift of $G$}, with vertex set $V(G)\times\{-1,1\}$. The vertices $(u,x)$ and $(v,y)$ are adjacent iff $(u,v) \in E(G)$, and $x \cdot y = s(u,v)$. The corresponding signed adjacency matrix$A_{G,s}$ is a symmetric $\{-1,0,1\}$-matrix, with $(A_{G,s})_{u,v} = s(u,v)$ if $(u,v) \in E$, and $0$ otherwise.