# How would I convert an arithmetic circuit into a system of bilinear equations?

Given an arithmetic circuit, are there any examples of turning it into a system of bilinear equations, with the end goal of turning it into a matrix?

For example, if the wires labeled as variables $$x$$ and $$y$$ are the inputs of a multiplication gate, whose output is $$z$$, then you would obtain the equation $$x\cdot y - z = 0$$. Similarly for addition gates. Overall, you would get a system of $$N$$ (non-homogeneous) quadratic equations in $$n$$ variables, where $$N$$ is the numbers of gates and $$n$$ is the number of wires.