- #1
AxiomOfChoice
- 533
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I don't think this should be a very difficult question for people who are used to working with tensors, but I'm new to it, so I'm confused. The Wikipedia article on the electromagnetic field tensor [itex]F^{\mu \nu}[/itex] asserts that
[tex]
F_{\mu \nu} F^{\mu \nu} = 2 \left( B^2 - \frac{E^2}{c^2} \right).
[/tex]
But if you look at the way they've written out [itex]F_{\mu \nu}[/itex] and [itex]F^{\mu \nu}[/itex] in matrix form, there is no way you get that when you just simply multiply the two matrices together. I mean, how can one obtain a constant from multiplying two square matrices (that aren't one-by-one, obviously) together? What am I missing here?
(The relevant Wikipedia article is http://en.wikipedia.org/wiki/Electromagnetic_tensor" .)
[tex]
F_{\mu \nu} F^{\mu \nu} = 2 \left( B^2 - \frac{E^2}{c^2} \right).
[/tex]
But if you look at the way they've written out [itex]F_{\mu \nu}[/itex] and [itex]F^{\mu \nu}[/itex] in matrix form, there is no way you get that when you just simply multiply the two matrices together. I mean, how can one obtain a constant from multiplying two square matrices (that aren't one-by-one, obviously) together? What am I missing here?
(The relevant Wikipedia article is http://en.wikipedia.org/wiki/Electromagnetic_tensor" .)
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