Matrices with Prescribed Entries and Eigenvalues. II
G. N. de Oliveira · SIAM Journal on Applied Mathematics · 1973
It is proved that there exists an n-square matrix (over an appropriate field) with prescribed eigenvalues and n prescribed entries except in the following cases : (i) the n prescribed entries are the principal entries, (ii) the n prescribed entries are on a row or column and the nonprincipal ones are zero.