For ideal polarizers with successive transverse transmission directions ${\theta }_j$, the Jones matrix is the rank-one orthogonal projection $P_j={\mathbf{u}}_j{\mathbf{u}}_j^{\mathsf{T}}$. The identity ${\mathbf{u}}_j^{\mathsf{T}}{\mathbf{u}}_{j-1}=\cos ({\theta }_j-{\theta }_{j-1})$ reduces the transmitted probability amplitude analogue, here the optical complex amplitude, to a product of projections. For unpolarized light, the first element transmits half the incident light intensity, giving the displayed product. For a specified incident linear polarization, replace the first half-factor with its actual projection.

A localized magnetic source described at leading nonvanishing dipole order by a magnetic dipole moment. A small current loop is one classical model. The source object, its moment vector and the resulting magnetic dipole field are distinct concepts. At large distance from a source with nonzero dipole moment, higher multipoles give smaller corrections; if the dipole moment vanishes, a higher-order term can lead instead.

Subtract a cylinder of current density $\mathbf{J}$ occupying the cavity from a complete current-carrying cylinder. Inside each cylinder, $\mathbf{B}={\mu }_0\mathbf{J}\times \mathbf{r}/2$. The difference is independent of observation point and equals ${\mu }_0\mathbf{J}\times \mathbf{b}/2$, where $\mathbf{b}$ is the offset of the cavity axis. This assumes parallel axes, uniform current density in the remaining metal, and negligible end effects.

A magnetostatic coupling caused by correlated roughness at interfaces of separated ferromagnetic films. Its tendency toward parallel alignment can modify a pseudo spin valve switching loop; it is not itself interlayer exchange.

The magnetic moment approached when the available magnetic degrees of freedom are fully aligned.

The observation-timescale-dependent temperature below which a magnetic configuration no longer relaxes readily during a measurement. For exchange bias it can mark stable pinning of antiferromagnetic interfacial domains and can be below the bulk Néel temperature. It is not identical to the thermodynamic onset of magnetic order.