Let's suppose that $h_1$, $h_2$, $b_1$ and $b_2$ are vectors of length $L\times 1$.
Where $h_1$ and $h_2$ are real and unknowns and $b_1$ and $b_2$ are known complexes
Is it possible to solve this expression?
$$h_1^T\times b_1=h_2^T\times b_2$$
I tried to see it as... $$(1\times L)\times (L \times 1)= (1\times L)\times (L \times 1)$$ then becomes $$(1\times L)= (1\times L)\times (L \times 1) \times (1\times L)$$ which indicates that $b_1$ and $b_2$ needs to be a matrix dimension. However linear algebra rule doesn't permit such move.
I want to see if I can find the relationship between $h_1$ and $h_2$. The most logical way is to move one $b$ to another side, but since they are vectors I have no idea how to.