Sorry for inaccuracy. I have an expression in form:

w = <a₁ b₂ J₁ + a₂² J₃ + ..., b₁² J₂ + ..., ...>

where w, a, b and J are n-dimension vectors. Note that the vector J enters to it linearly. I want to obtain the following form of this equation:

w = F(a, b).J

where unknown matrix F depends only of vectors a and b, i.e. i need find matrix F.