Various 3x3 Nonnegative Matrices with Prescribed Eigenvalues and   Diagonal Entries
  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. 
Jin Ok Hwang and Donggyun Kim
math.SP math.RA