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

$${\displaystyle y^{T}A_{i}x=g_{i},}$$

where, i is an integer whose value ranges from 1 to the number of equations, each ${\displaystyle A_{i}}$ is a matrix, and each ${\displaystyle g_{i}}$ is a real number. Systems of bilinear equations arise in many subjects including engineering, biology, and statistics.