Lorentz Transformation

  • Thread starter yukcream
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  • #1
yukcream
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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
 

Answers and Replies

  • #2
quantumdude
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Start by writing down the matrix representation of a general Lorentz transformation.

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

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

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 [itex]T^{\mu}_{\nu}[/itex] equals itself, unless there is something else implied by the { } braces.
 
  • #3
yukcream
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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
quantumdude
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yukcream said:
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. :tongue2:

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

OK, so now you're asking if [itex]T[/itex] is equal to its own inverse. Again, try to write down the matrix and see if that is so.
 
  • #5
yukcream
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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
 

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