In mathematics, the **determinantal conjecture** of Marcus (1972) and de Oliveira (1982) asks whether the determinant of a sum *X* + *Y* of two *n* by *n* normal complex matrices *X* and *Y* lies in the convex hull of the *n*! points Π_{i} (*x*_{i} + *y*_{σ(i)}), where the numbers *x*_{i} and *y*_{i} are the eigenvalues of *X* and *Y*, and *σ* is an element of the symmetric group *S*_{n}.