Coherency matrix
= Coherency matrix
{title2=$C_{ij}=\langle E_iE_j^*\rangle$}
The optical <coherency matrix> records the second moments of transverse <complex amplitudes>. Normalize its trace to <light intensity>. Under a deterministic <Jones matrix> $M$, $C\mapsto MCM^\dagger$. <Unpolarized light> has $C=(I_0/2)I_2$, so its output intensity is $(I_0/2)\operatorname{tr}(MM^\dagger)$; it cannot be represented by one fixed <Jones vector>.