I'm halfway through a question on a past differential geometry exam, and suddenly in comes a matrix g a member of SL(2,C) (where C denotes the complex numbers)(adsbygoogle = window.adsbygoogle || []).push({});

Now, I can't remember how to express a general element of this group: I know the matrix must be

[tex]\left(\begin{array}{cc}a&b\\c&d\end{array}\right)[/tex] such that ad-bc=1, but can this be expressed in a more precise way in the complex case (i.e. with fewer than four unknowns, maybe by utilising the complex conjugate)?

I've tried looking on the internet, but to no avail. I would really appreciate someone helping, since I could do with getting on with the question!

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# General element of SL(2,C)

**Physics Forums | Science Articles, Homework Help, Discussion**