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 T A i x = g i , {\displaystyle y^{T}A_{i}x=g_{i},} where, i is an integer whose value ranges from 1 to the number of equations, each A i {\displaystyle A_{i}} is a matrix, and each g i {\displaystyle g_{i}} is a real number. Systems of bilinear equations arise in many subjects including engineering, biology, and statistics.
See also Systems of linear equations
References Charles R. Johnson, Joshua A. Link 'Solution theory for complete bilinear systems of equations' - http://onlinelibrary.wiley.com/doi/10.1002/nla.676/abstract Vinh, Le Anh 'On the solvability of systems of bilinear equations in finite fields' - https://arxiv.org/abs/0903.1156 Yang Dian 'Solution theory for system of bilinear equations' - https://digitalarchive.wm.edu/handle/10288/13726 Scott Cohen and Carlo Tomasi. 'Systems of bilinear equations'. Technical report, Stanford, CA, USA, 1997.- ftp://reports.stanford.edu/public_html/cstr/reports/cs/tr/97/1588/CS-TR-97-1588.pdf