For anisotropic materials, the field relationships at any point differ for different directions of propagation. This means that a 3-by-3 tensor is necessary to properly define the constitutive relationships. If this tensor is symmetric, the material is often referred to as reciprocal. In such cases, rotate the coordinate system such that a diagonal matrix results. If two of the diagonal entries are equal, the material is
uniaxially anisotropic. If none of the elements have the same value, the material is
biaxially anisotropic (
Ref. 2). Anisotropic parameters are needed, for example, to examine permittivity in crystals (
Ref. 2) and when working with conductivity in solenoids.