Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate. P(a) = tr(D.Pra) The problem is, since I have then a product between de density matrix tr(D.Pra), Pra would have to be a matrix of the same rank of D, write ? To calculate then the tr. What is the right way to construct the projection ? Transform the state, a vector, into a matrix ? Beeing a matrix with just one element in the main diagonal for each of the a directions relative to each eingenstate ? I'm a new member, so I'm not used to ask questions online. Thank you.