I'm trying to express the tensor equation [itex]F'^{\mu\nu}=\Lambda^{\mu}_{\sigma}\Lambda^{\nu}_{ \rho }F^{\sigma\rho}[/itex] in matrix form. Here the indices range from 0 to 3, so we need 4 by 4 matrices. Let F', F, and [itex]\Lambda[/itex] be the matrices associated with the tensors appearing in our equation. Which of the following is the correct matrix translation of the tensor equation?(adsbygoogle = window.adsbygoogle || []).push({});

[itex]F'=\Lambda F \Lambda[/itex]

[itex]F'=\Lambda \Lambda F[/itex]

[itex]F'=\Lambda^{\top} F \Lambda[/itex]

[itex]F'=\Lambda F \Lambda^{\top}[/itex]

Or something else entirely?

I tried testing some of these out on the actual four-by-four matrices, but the algebra got too cumbersome. Usually when I figure out what order to put things in and where to put the transposes, I'm in a situation where I'm dealing with matrices and vectors, so that if you put it in the wrong order then the numbers of rows and columns don't match up. But in this case everything is four-by-four, so there is plenty of room for error.

Any help would be greatly appreciated.

Thank You in Advance.

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# Writing Tensor Equations in Matrix Form

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