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Feb28-13, 09:35 AM
P: 38
In the study of electric and magnetic fields, two equations are called the constitutive relations of the medium (the vacuum, for example):

[itex]\mathbf{D} = \mathbf{\epsilon} \cdot \mathbf{E}\\
\mathbf{B} = \mathbf{\mu} \cdot \mathbf{H}[/itex]

But in a generic medium (non linear, non isotropic, non homogeneous) [itex]\mathbf{\epsilon}[/itex] and [itex]\mathbf{\mu}[/itex] are tensors. Now, why not matrices with dimension 3x3? [itex]\mathbf{E}[/itex] and [itex]\mathbf{H}[/itex] are "simple" three-dimensional vectors. I know that a matrix is a particular case of a tensor, but so why do we never use the term "matrix" in this context?
A matrix could exist only if a particolar system of coordinates is defined, whereas a tensor can always exist: is it the reason for calling [itex]\mathbf{\epsilon}[/itex] and [itex]\mathbf{\mu}[/itex] tensors and not just matrices?
Thank you anyway!

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