Not sure what to call this problem, but say I have a bunch of equations like this: v1'*M*v1 = c1 v2'*M*v2 = c2 ... M is an unknown square matrix and is the same in every equation. v is a vector and c is a scalar, these are different in each equation. I can have as many of these as I need. Is there a clever way to solve for M? I wrote out the 2x2 case and can solve it if I take apart M, but I'd like a more elegant extensible solution if one exists. I hope my question makes sense. Thanks.