# Pauli-decomposition

24 May 2017any complex \(2\times2\)-matrix \(A_{\mu\nu}\) (for instance, the lensing Jacobian) can be decomposed in terms of 3 Pauli-matrices \(\sigma^{(n)}_{\mu\nu}\) and the unit matrix \(\sigma^{(0)}_{\mu\nu}\), \(A_{\mu\nu} = \sum_{n=0}^3 a_n\sigma^{(n)}_{\mu\nu}.\) can you show that the coefficients are given by \(a_n = (A_{\mu\nu}\sigma^{(n)}_{\nu\mu})/2\) and that the set of matrices is a complete basis?