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I tried to write it in latex, but apparently it's too complicated for this website to read the code. Here is the link to it: https://ibb.co/dA4cV5

Anyway, it has been 2 years since I got it. Now, I don't remember what book I got it from. I'm 100% certain that I got it from a book! However, it's also possible that the book got the result from another original paper. Either way, I just want to look for a source that shows the derivation I have in the picture starting from "First, take $\Omega\in GL_m(\Bbb R)$..." This is a generalization of the Lorentz group. I know the J is a little bit different from the J in Lorentz group, but after you find $\theta$ in that case, with a little modification, you can find the $\theta$ in Lorentz group pretty easily.

I literally have been looking for the book and the paper for days but without any luck. Maybe with a few more pairs of eyes is what I need. Maybe some of you math experts will know what paper to look for right away when you see the derivation. Please help!

Some possible key searches include Lorentz group, Lorentz decomposition, Minkowski space, Lorentz boost...

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    $\begingroup$ A side note, It's probably not that the Latex needed is "too complicated" for the site/Mathjax, but rather that certain macros (like \R) aren't in use here. $\endgroup$
    – pjs36
    Commented Jun 22, 2017 at 16:38
  • $\begingroup$ Are you sure it's even from a book or a paper? I see several (non-mathematical) issues in this that make me hope otherwise. And I second what @pjs36 said as this site definitely has more complicated MathJax expressions rendered throughout it. Actually, I think I see a mathematical issue now but I can't tell because the image is too blurry. Does that say $B = -D\sigma$ while also saying $\sigma \in \Bbb R^n$, $B$ is $(n-1) \times 1$, and $D \in \Bbb R$? Or does that say $D$ is $1 \times (n-1)$? Either way, $B = -D\sigma$ wouldn't make sense. $\endgroup$
    – user307169
    Commented Jun 22, 2017 at 16:39
  • $\begingroup$ I'm definitely certain. The whole proof of this is actually 2 pages long. I actually hand written it, but I need the original source to cite it. It's not apparent at first look. I had no clue either until I saw it in the book. Someone must have taken A LOT of time to come up with a clever way of generalizing Lorentz group. $\endgroup$
    – Phu Nguyen
    Commented Jun 22, 2017 at 16:44
  • $\begingroup$ Well.. I can't decipher that sentence at the top that begins with "Furthermore." Maybe someone else will have better luck, but it'd probably be best to post a clearer pic or try the LaTeX again. $\endgroup$
    – user307169
    Commented Jun 22, 2017 at 16:46
  • $\begingroup$ You're right. I made a mistake. It's supposed to be $C$ is $1 \times (n-1)$. Nice catch and thanks! I posted a new picture with an updated version. $\endgroup$
    – Phu Nguyen
    Commented Jun 22, 2017 at 17:00

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I just found the book I've been looking for. It's call Special Relativity by Michael Tsamparlis. The proof starts on page 26 (section 1.7).

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