In mathematics, the determinantal conjecture of and asks whether the determinant of a sum A + B of two n-by-n normal complex matrices A and B lies in the convex hull of the n! points à<sub>i</sub> (û(A)<sub>i</sub> + û(B)<sub>ÃÂ(i)</sub>), where the numbers û(A)<sub>i</sub> and û(B)<sub>i</sub> are the eigenvalues of A and B, and àis an element of the symmetric group S<sub>n</sub>.