Symmetric matrices defined by plane vector sequences

Motivated by a work of Fu-So-Song, we associate a symmetric matrix $A$ to a plane vector sequence $v$ and give a formula to find the signature of $A$ in terms of the sequence $v$. When $A$ is nonsingular, we interpret the relation between $A$ and $A^{-1}$ from a topological viewpoint. Finally, we associate an omnioriented quasitoric orbifold $X$ of real dimension four to the sequence $v$ and show that $A^{-1}$ is the intersection matrix of the characteristic suborbifolds of $X$.