Institution: Stanford University, Department of Computer Science

Title: Systems of Bilinear Equations

Author: Cohen, Scott

Author: Tomasi, Carlo

Date: April 1997

Abstract: How hard is it to solve a system of bilinear equations? No solutions are presented in this report, but the problem is posed and some preliminary remarks are made. In particular, solving a system of bilinear equations is reduced by a suitable transformation of its columns to solving a homogeneous system of bilinear equations. In turn, the latter has a nontrivial solution if and only if there exist two invertible matrices that, when applied to the tensor of the coefficients of the system, zero its first column. Matlab code is given to manipulate three-dimensional tensors, including a procedure that finds one solution to a bilinear system often, but not always.

http://i.stanford.edu/pub/cstr/reports/cs/tr/97/1588/CS-TR-97-1588.pdf