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Homework Help: Lorentz Transformation

  1. Sep 27, 2005 #1
    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~

  2. jcsd
  3. Sep 27, 2005 #2

    Tom Mattson

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

    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.

    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.
  4. Sep 27, 2005 #3
    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
  5. Sep 27, 2005 #4

    Tom Mattson

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    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 [itex]T[/itex] is equal to its own inverse. Again, try to write down the matrix and see if that is so.
  6. Sep 27, 2005 #5
    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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