Is T = T^-1 in Lorentz Transformations for 4 Vectors?

[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

 

[quantumdude]

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

I am not sure wheather
matrix T^v_u = {T^u_v}^-1

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.

or T^v_u = {T^v_u} is true?

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.

 

[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

 

[quantumdude]

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

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

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

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.

 

[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