Consider two coils with inductances $L_1$ and $L_2$, coupled by mutual inducance $M$. The inductors have series resistance $R_1$ and $R_2$

This circuit can be represented by the following equivalent circuit:

INSERT FIGURE HERE

The impedance matrix of the circuit is given by:

\begin{align} Z = \begin{bmatrix} R_1+j\omega L_1 & j \omega M \\ j \omega M & R_1+j\omega L_ 2 \\ \end{bmatrix} \end{align}

with $\omega$ the angular frequency.