CEID Seminar & Social Hour: “Recent ventures on matrix eigenvalues”, Michael Tsatsomeros, Professor, Dept. Mathematics & Statistics, Washington State University, USA

Τίτλος:  Recent ventures on matrix eigenvalues

Ομιλητής: Michael Tsatsomeros, Professor, Dept. Mathematics & Statistics, Washington State University, USA

Ημερομηνία-χώρος: Παρασκευή 10 Νοεμβρίου,  3-5μμ, ΤΜΗΥΠ, αμφιθέατρο Γ

Περίληψη: The talk will present some recent research on aspects of the algebraic eigenvalue problem, which is of critical importance in many applications. We will first provide some motivating remarks and background and will then focus on two topics. Part 1 regards “localizing” the spectrum (that is, computing a region in the complex plane that contains the eigenvalues). Part 2 involves “manipulating” matrices via feedback in order to dictate the behavior of dynamical systems. Specifically, in Part 1, we introduce an enveloping region E(A) in the complex plane that contains the eigenvalues of a complex matrix A. E(A) is the intersection of an infinite number of regions bounded by elliptic curves. The notion and method of construction of E(A) generalize the numerical range, F(A), which is known to be the intersection of an infinite number of half-planes; as a consequence, E(A) is contained in F(A) and represents a significant improvement in localizing the spectrum of A with minimal additional numerical effort. In Part 2, entitled “Rank One Perturbations for Cone Reachability and Holdability”, we propose a choice of feedback control in a linear control system in order for the trajectory to eventually enter the nonnegative orthant and remain therein for all time thereafter. This is achieved by imposing the strong Perron-Frobenius property and involves altering the eigenvalues, as well as the left eigenvectors via rank one perturbations.

Σχετικά με τον ομιλητή: Michael Tsatsomeros is a Professor of Mathematics at Washington State University since 2001. He is a graduate of the University of Connecticut (Storrs, 1990), Concordia University (Montreal,1986) and the University of Patras (1984), and has held positions at the Universities of Wisconsin, Regina, Victoria, the College of William & Mary and the Indian Institute of Technology Madras. Michael’s research interests lie in linear algebra, matrix analysis, especially the theory of nonnegative matrices and their generalizations. Particular interests include the numerical range; graphs and patterns associated with matrices; numerical linear algebra; applications in dynamical systems, control theory, data analysis, machine learning and artificial intelligence. He has served as an editor-in-chief of the Electronic Journal of Linear Algebra and is an Associate Editor of Linear Algebra and Its Applications since 2004. Michael has supervised 12 PhD students and is the co-author of the recent monograph Matrix Positivity.

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