I have three complex variables
$$x=\begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}'$$
two complex knowns
$$d=\begin{bmatrix} d_1 & d_2 \end{bmatrix}'$$
and two equality constraints
$$x_1x_2 = d_1$$
$$x_1x_3 = d_2$$
I would like to know how to represent the equality constraints in linear matrix inequality (LMI) form so that I can use an SDP solver.
P.S. This is my first time posting a question, so tips on refining the question itself are also appreciated.