Inductance matrix ($\mathbf{\lambda }=\mathbf{Li}$)

An inductance matrix relates magnetic flux linkages to electric currents in a linear model of coupled inductors. For reciprocal two-coil coupling, $\mathbf{L}=\left(\begin{array}{cc}{L}_1& M\\ M& L_2\end{array}\right)$. Its stored magnetic energy is ${\mathbf{i}}^T\mathbf{Li}/2$. With $L_1,L_2>0$, it is a positive-definite matrix exactly when $M^2<L_1{L}_2$. Equality is a singular limiting model requiring separate treatment.