Brute force was my initial plan :shy: problem is: Only using comm and anti-comm I get a whole bunch of possible solutions (like e.g. \sigma_x'=-\sigma_x=(0 & -1 \\ -1 & 0) and \sigma_y'=-sigma_y=(0 & i \\ -i \\ 0) ) also obeying these commutation relations.
I would like to restrict these...
Does anyone know of an alternative way of calculating the Pauli spin matrices \mbox{ \sigma_x} and \mbox{ \sigma_y} (already knowing \mbox { \sigma_z} and the (anti)-commutation relations), without using ladder operators \mbox{ \sigma_+} and \mbox{ \sigma_- }?
Thanks!