Inductance matrix (source code)

= Inductance matrix
{title2=$\boldsymbol\lambda=\mathbf L\mathbf i$}

An <inductance matrix> relates <magnetic flux linkages> to <electric currents> in a linear model of <coupled inductors>. For reciprocal two-coil coupling, $\mathbf L=\left(\begin{smallmatrix}L_1&M\\M&L_2\end{smallmatrix}\right)$. Its stored <magnetic energy> is $\mathbf i^T\mathbf L\mathbf i/2$. With $L_1,L_2>0$, it is a <positive-definite matrix> exactly when $M^2<L_1L_2$. Equality is a singular limiting model requiring separate treatment.