# Tools for solving bilinear problems

I have a general question regarding the tools for solving bilinear problems. I have a bilinear problem of the form $y_k^H A_{kj} x_j = 0$ for $k \ne j$ and $y_k^H A_{kj} x_j \ne 0$ for $k=j$. Here, $x$ and $y$ are complex variables. $A_{kj}$ are given complex matrix. I searched for methods to solve bilinear problems in internet but did not find one. I think it should be either something obvious that it do not appear in the internet or may be i am searching with the wrong term.

edit: methods for solving nonlinear problems can be applied. But i think there should be something better because of the partly linear nature of the problem.

kronecker products are something that i think is related to this (because vectorization of the equation results in the kronecker product of the variables) But i could not find something like solving system of equations using kronecker products.

Can you tell me what kind of mathematics books can i look in for such problems. is kronecker product one such tool?

Any recommendation for a book or tutorials will be of much help.

I don't understand your notation. Is $y_k$ a scalar, or one of a set of vectors? I.e. is A a 2x2 matrix or a rank 4 tensor? – user7530 Nov 1 '11 at 17:18
$y_k$ is a column vector. $A_{kj}$ is a matrix. – karthik Nov 12 '11 at 15:00