A is a square matrix. x, b are vectors. I know for Ax=b, that given b, there are an infinite number of pairs (A, x) which satisfy the equation. I'm wondering if the same is true for xAx=b. in particular, what if (x, A, b) are all stochastic vectors/matrices (i.e the entries of b and x add to 1, and so do each column of A). Would that make it so there was a single solution (A,x) for a given b? Thanks.