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## Main Question or Discussion Point

Hello!

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

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!

Emily

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!

Emily