A Problem in Georgi's Lie algebras in particle physics

[zahero_2007]

Can some one please explain to me equation 2.35 on page 49 in the textbook "Lie algebra in particle physics " How can he extract the 2 Transformation matrices outside the trace operator ?I think there is something wrong
Sorry I do not know how to use latex

 

[naima]

in 2.34 Ta and Td are vectors of matrices. And Lad a vector of numbers so Lad Td is not a matrix product but a scalar product. You can put Lad near Td.
It would be the same with another index for Tb. L and L^-1 are the same
You can then multiply, take the traces and extract the numbers (not matrices)

I hope i wrote not too many wrong things!

 

[zahero_2007]

I see , Thanks a lot naima .

 

[naima]

When
Ta -> T'a = L [Lac.Tc] L^-1
Tb -> T'b = L [Lbd.Td] L^-1
then
TaTb -> L [ (Lac.Tc)(Lbd.Td)] L^-1
You know that Tr(AB) = Tr (BA) so when you take the trace of the rhs you get
Tr ((Lac.Tc)(Lbd.Td))
Lac and Lbd are numbers and Rc Tc are matrices and as trace is linear so you get 2.35