Editing Polarizability (section)

===Tensor===
To describe anisotropic media a polarizability rank two [[tensor]] or <math>3 \times 3</math> [[Matrix (mathematics)|matrix]] <math>\alpha</math> is defined,

:<math> \mathbb{\alpha} = 
\begin{bmatrix}
\alpha_{xx} & \alpha_{xy} & \alpha_{xz} \\
\alpha_{yx} & \alpha_{yy} & \alpha_{yz} \\
\alpha_{zx} & \alpha_{zy} & \alpha_{zz} \\
\end{bmatrix}
</math>

so that:

:<math>
\mathbf{p} = \mathbb{\alpha} \mathbf{E}
</math>

The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of <math>\alpha_{yx}</math> here means that an electric-field applied in the <math>x</math>-direction would strongly polarize the material in the <math>y</math>-direction. Explicit expressions for <math>\alpha</math> have been given for homogeneous anisotropic ellipsoidal bodies.<ref>Electrodynamics of Continuous Media, L.D. Landau and E.M. Lifshitz, Pergamon Press, 1960, pp. 7 and 192.</ref><ref>C.E. Solivérez, ''Electrostatics and Magnetostatics of Polarized Ellipsoidal Bodies: The Depolarization Tensor Method'', Free Scientific Information, 2016 (2nd edition), {{ISBN|978-987-28304-0-3}}, pp. 20, 23, 32, 30, 33, 114 and 133.</ref>