In mathematics, the determinantal conjecture of Marcus (1972) and de Oliveira (1982) asks whether the determinant of a sum A + B of two n by nnormal complex matricesA and B lies in the convex hull of the n! points Πi (λ(A)i + λ(B)σ(i)), where the numbers λ(A)i and λ(B)i are the eigenvalues of A and B, and σ is an element of the symmetric group Sn.
References
de Oliveira, G.N. (1982), "Research problem: Normal matrices", Linear and Multilinear Algebra, 12: 153–154
Marcus, Marvin (1972), "Derivations, Plücker relations, and the numerical range", Indiana University Mathematics Journal, 22: 1137–1149, ISSN0022-2518, MR0314862
