Let O be a measurement operator for the of dots facing upwards on a 6-sided 'quantum' die-- a die that can be put into superpositions of states and then measured. The set of possible outcomes is {1,2,...6}. In quantum theory these are supposed to be the eigenvalues of the measurement operator, O. In order words, the eigenvalues are Oq ε{1..6} in the eigen equation O l q> = Oq l q> where l q> are the states corresponding to the measured e. values What is the expression for the operator O, in the bra-ket notation?