Since there are numerous valid definitions of two parameters depending on the reference point used, the reference currents and voltages used as the basis of further work will be described here. The diagram below shows the orientation of reference currents and voltages.
This is basically a set of definitions that are referenced by other posts. Common two port parameters are admittance (Y) parameters, impedance (Z) parameters and hybrid (H) parameters. With reference to the above diagrams, the matrix equations for these parameters are shown below.
\begin{equation}
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
i_1 \\
i_2
\end{bmatrix}
= Y
\begin{bmatrix}
v_1 \\
v_2
\end{bmatrix}
\end{equation}
\begin{equation}
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
v_1 \\
v_2
\end{bmatrix}
= Z
\begin{bmatrix}
i_1 \\
i_2
\end{bmatrix}
\end{equation}
\begin{equation}
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
v_1 \\
i_2
\end{bmatrix}
= H
\begin{bmatrix}
i_1 \\
v_2
\end{bmatrix}
\end{equation}