System of bilinear equations

In mathematics, a system of bilinear equations is a special sort of system of polynomial equations, where each equation equates a bilinear form with a constant (possibly zero). More precisely, given two sets of variables represented as coordinate vectors $x$ and y, then each equation of the system can be written $$y^TA_ix=g_i,$$ where, $i$ is an integer whose value ranges from 1 to the number of equations, each $$A_i$$ is a matrix, and each $$g_i$$ is a real number. Systems of bilinear equations arise in many subjects including engineering, biology, and statistics.