Why Do Lorentz Transforms Look Like This?

[AndrewGRQTF]

We have all seen Lorentz transformations being written like this $\Lambda ^\mu\;_\nu$, but why are they never written as $\Lambda _\nu\;^\mu$?

 

[Ibix]

You do. Sean Carroll, at least, uses SW/NE indices to indicate an inverse transform.

It's just convention, anyway.