  In this paper, we answer the various forms of nonnegative inverse eigenvalue
problems with prescribed diagonal entries for order three: real or complex
general matrices, symmetric stochastic matrices, and real or complex doubly
stochastic matrices. We include the known cases, the symmetric matrices and
real or complex stochastic matrices, to compare the other results and for
completeness. In addition, for a given list of eigenvalues, we compute the
exact range for the largest value of the diagonal entries of the various
nonnegative matrices.
