- #1

AxiomOfChoice

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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

(The relevant Wikipedia article is http://en.wikipedia.org/wiki/Electromagnetic_tensor" [Broken].)

[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" [Broken].)

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