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Mathematics Colloquium: Spectrum Localization for Complex Matrices
4:00 p.m., Neill Hall 5W
Abstract: Using the notions of the numerical range, Schur complement and unitary equivalence, an inequality is obtained satisfied by each eigenvalue of a complex matrix A. In turn, this inequality gives rise to a region in the complex plane that contains the spectrum of A, improving classical results by Bendixson and Wielandt.