How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ or $\epsilon$ (permeability or permittivity) is a tensor?

I've read that in some materials, $\mu$ can be a tensor, not a mere scalar. (I haven't actually dealt with tensors before, but I'm assuming for my purposes here, it is synonymous with "matrix".)

I'm not sure if the same holds for $\epsilon$, but I'm assuming it might there too.

I'm fine with thateither of those, but then I'm wondering what the formula

$$\epsilon\,\mu = \frac{1}{c_m^2}$$

turns into when $\mu$ is a tensordealing with tensors? ($c_m$ being the speed of light in the medium)

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asked Dec 26, 2016 at 19:32

user541686

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How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ is a tensor?

I've read that in some materials, $\mu$ can be a tensor, not a mere scalar. (I haven't actually dealt with tensors before, but I'm assuming for my purposes here, it is synonymous with "matrix".)

I'm fine with that, but then I'm wondering what the formula

$$\epsilon\,\mu = \frac{1}{c_m^2}$$

turns into when $\mu$ is a tensor?

electromagnetism speed-of-light

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How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ or $\epsilon$ (permeability or permittivity) is a tensor?

How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ is a tensor?

How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ or $\epsilon$ (permeability or permittivity) is a tensor?

How does $\epsilon \mu = 1/c_m^2$ change when $\mu$ is a tensor?