Some remarks on a conjecture of de Oliveira
Some years ago the present reviewer [Linear Multilinear Algebra 12, 153- 154 (1982)] conjectured that if A and B are normal matrices then the determinant of \(A+B\) lies in the convex hull of the complex numbers \(\prod_{i}(\alpha_ i+\beta_{\sigma (i)})\). Here the \(\alpha_ i's\) and the \(\beta_ i's\) are the eigenvalues of A and B respectively, and \(\sigma\) runs over the symmetric group of degree n. The authors prove that the conjecture is true in some particular cases as, for example, when \(| \alpha_ 1| =...=| \alpha_ n| =| \beta_ 1| =...=| \beta_ n|\).
scientific article; zbMATH DE number 4075276