# Lorentz Transformation

1. Sep 27, 2005

### yukcream

I am not sure wheather
matrix T^v_u = {T^u_v}^-1
or T^v_u = {T^v_u} is true?
T is a lorentz transformation for 4 vector~

Yuk

2. Sep 27, 2005

### Tom Mattson

Staff Emeritus
Start by writing down the matrix representation of a general Lorentz transformation.

In matrix language, that is $T^T=T^{-1}$. In other words, you are asking if the transpose of $T$ equals the inverse of $T$.

Try writing it out explicitly and see if it does.

Is there a typo here? Because here you just seem to be asking if $T^{\mu}_{\nu}$ equals itself, unless there is something else implied by the { } braces.

3. Sep 27, 2005

### yukcream

It is great that you can understand my notation~ you are so smart!!

It is my fault that I want to ask is T^v_u = {T^v_u} -1?

thanks for help
yuk

4. Sep 27, 2005

### Tom Mattson

Staff Emeritus
Your notation is a lot like LaTeX, which is what I used to make my math symbols. So, I'm not really that smart. :tongue2:

OK, so now you're asking if $T$ is equal to its own inverse. Again, try to write down the matrix and see if that is so.

5. Sep 27, 2005

### yukcream

Actually T is a special transformation~ called Lorentz transformation. In 4 vector case they are not equal~ but my lecturer asked me to prove T = T inverse~ I wonder is there is any typing error in his assignment given? or the position of the indexs may affect the result? They are not the same in fact!

yuk yuk