System of bilinear equations

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (November 2012) (Learn how and when to remove this message)

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.