Matrices with prescribed entries and eigenvalues. I
G. N. de Oliveira · Proceedings of the American Mathematical Society · 1973
It is proved that there exists a matrix (over an appropriate field) with prescribed eigenvalues and a prescribed nonprincipal diagonal. It is also proved that there exists an $n \times n$ matrix, over an arbitrary field, with prescribed eigenvalues and with $n - 1$ prescribed arbitrary entries.