Given a graph $G=(V,E)$ and it's edges space $\mathcal{E}(G)$ in the book by Diestel it defines
given two edges sets $F,F'$ and their coefficients $\lambda_{1},...,\lambda_{m}$ and $\lambda_{1}',...,\lambda_{m}'$ $\langle F,F'\rangle=\lambda_{1}\lambda_{1}'+...+\lambda_{m}\lambda'_{m} \in \mathbb{F}_{2}$.
Now i'm guessing they force the sum to be modulo $2$ otherwise clearly it does not need to be right? Secondly what is the importance mathematically of defining this product in this way?
I am new to vector spaces, and have found that a similar notation is used in "inner product spaces" so i'm guessing the product defined above would be an inner product space? Which would explain why it's elements are mapped to $\mathbb{F}_{2}$.