Algebra

   

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 3 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.

Comments: 11 Pages.

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Submission history

[v1] 2018-05-20 05:12:52
[v2] 2018-05-24 17:28:18
[v3] 2018-06-01 17:03:00
[v4] 2018-06-02 05:19:02
[v5] 2018-06-06 15:20:33
[v6] 2018-06-12 05:12:19
[v7] 2018-10-04 19:34:38

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