On the eigenvalues of matrices with prescribed upper triangular part

Consider a matrix D=[D_i,j] partitioned in submatrices D_i,j where the submatrices D_i,iare square. This paper studies the possible eigenvalues of D, when the blocks D_i,j, with i≤j, are fixed, and the other blocks vary. The result obtained generalizes twotheorems already known.