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 ∆. Let ∆S be the restriction of ∆ to determinants of sums of symmetric normal matrices. In this paper, we conjecture that ∆S has the same boundary as ∆. We prove the conjecture under the restriction that at least one of the two matrices has distinct eigenvalues. If this conjecture is true then proving the Marcus-de Oliveira conjecture for symmetric normal matrices would prove it for the general case. This paper builds on work in .
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