Electronic Theses and Dissertations

# Progress on the Marcus-de Oliveira Determinantal Conjecture

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dc.date.accessioned2017-04-12T20:22:12Z
dc.date.available2017-04-12T20:22:12Z
dc.date.issued2017-04-12
dc.identifier.urihttp://hdl.handle.net/10415/5587
dc.description.abstractWe discuss the well known conjecture of Marcus and de Oliveira of the determinant of the sum of normal matrices. We present the motivation of this conjecture, along with detailed history of its origin. Then we compile several situations in which the conjecture holds. That is the matrices satisfying the equation: $$\Delta(A,B) \subseteq \co \{\prod_{i=1}^n (\alpha_i + \beta_{\sigma(i)}) : \sigma \in S_n\}$$ We also display further relations and links between Marcus and de Oliveira conjecture and other topics and conjectures, and indicate the cases that will be implied from them. Moreover, we provide some consequential results in various aspects regarding this conjecture.en_US
dc.subjectMathematics and Statisticsen_US
dc.titleProgress on the Marcus-de Oliveira Determinantal Conjectureen_US
dc.typeMaster's Thesisen_US
dc.embargo.statusNOT_EMBARGOEDen_US
dc.contributor.committeeHolmes, Randall
dc.contributor.committeeNylen, Peter
dc.contributor.committeeAlbrecht, Ulrich