BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Localization of the Spectrum of a Matrix Tsatsomeros, Michael


New and old results will be presented on the Envelope, $E(A)$, which is a bounded region in the complex plane that contains the eigenvalues of a complex matrix $A$. $E(A)$ is the intersection of an infinite number of regions defined by elliptic curves. As such, $E(A)$ resembles and is contained in the numerical range of $A$, which is the intersection of an infinite number of half-planes. The Envelope, however, can be much smaller than the numerical range, while not being much harder to compute. The talk is based on joint work with Panos Psarrakos, Maria Adam and Katerina Aretaki.

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