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Lorentz Boost Applied to Faraday for a Static Electric Field

I include this calculation to illustrate that the very succinct Einstein notation for tensors should be understood as representing arrays, or matrices. Anyone learning general relativity should do a number of similar calculations in order to become comfortable with the notation. I make no apologies for errant minus signs — you should have done it yourself.

Write the first contraction in matrix form
Multiply matrices

Transpose, so that we can multiply rows by columns in the usual way.

Multiply matrices

Cancel terms, using the Lorentz factor

Transpose back


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