Analysis shows that determinant of two normal matrices lies in the convex hull of eigenvalue products, suggesting new insights into matrix theory.
Let A, B be n× n normal matrices with eigenvalues (a₁,…,aₙ), (b₁,…,bₙ), respectively. We show that (A+B) lies in the convex hull of ψₙ\∏ᵢ₌₁ⁿ(aᵢ+bψᵢ)\ if all eigenvalues of A, B are real, except for three eigenvalues of B.
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Yaroslav Shitov (2025) studied this question.
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