Determinantal conjecture

Short description: Mathematical conjecture

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 n normal complex matrices A and B lies in the convex hull of the n! points Π_i (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 S_n.

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, ISSN 0022-2518