# Spin density matrix

1. Aug 10, 2009

### baru

Could any one help me to understand how the spin density matrix is invariant under unitary transformation?

2. Aug 12, 2009

### tonyetc

hi,
if you mean how a general density matrix is invariant under unitary transformation, the consider that density matrices are used to evaluate mean values of an operator A, <A R>= Tr(AR), where R is the density matrix and Tr denotes the trace operation. Then performing a unitary transformation yields the same result: Tr(SAS^-1 SRS^-1) = Tr(SARS^-1) = Tr(S^-1SAR) = Tr(AR) because of invariance under cyclic permutation of the trace.
If you mean something else, please forget my answer and post again.
thanks