Help with Lorentz Transformation Notation & Matrix Entries

[grzz]

The symbol for a Lorentz transformation is sometimes Λ^α_β and sometimes Λ_μ^ν.

When Λ^α_β is shown by a matrix, the upper index denotes the entries in the rows and the lower index denotes the entries in the columns.

When Λ_μ^ν is shown by a matrix, does the upper index still denotes the entries in the rows?

Any help is much appreciated.

Thanks.

 

[Orodruin]

This depends on how you chose to represent the Lorentz transformation in matrix form, or more precisely, how you chose to represent covariant and contravariant vectors and how the Lorentz transformation acts on them.

 

[grzz]

Does it mean that when Λ^α_β acts on a contravariant vector x^β, then the upper index of Λ denotes the rows and when Λ_α^β acts on a covariant vector x_β, then it is the lower index which denotes the rows?

 

[dextercioby]

Yes, that's an accepted logic. Just remember that physicists don't put mu exactly over nu, it's always a space (it's either south-west-north-east or north west-south east, but never north south).

 

[Matterwave]

I'd like to also add that usually I see a prime on one of the indices to make it easier to figure out which frame to which the Lorentz transformation is transforming to.

 

[grzz]

I'd like to also add that usually I see a prime on one of the indices to make it easier to figure out which frame to which the Lorentz transformation is transforming to.

Thanks for all the replies!

Yes, 'Matterwave', I intended to put a prime on one of the indices of Λ to distinguish from which frame of reference and to which frame the Λ is transforming but I could not figure out the way to do it!