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The Perron-Frobenius Theorem revisited. From real to complex!

Title of the event The Perron-Frobenius Theorem revisited. From real to complex!
Series SonstigeVeranstaltungenMI
Organizer Mathematisches Institut
Speaker Prof. Hans Henrik Rugh
Speaker institution Universität Paris-Süd
Type of event Vortrag
Category Forschung
Registration required Nein
Details The celebrated Perron-Frobenius theorem for the existence of a leading positive eigenvalue of a positive matrix came to light in 1907. A plethora of proofs and generalizations have since appeared. I have selected a couple of significant ideas and events in this evolution with illustrations borrowed from dynamical systems and probability theory. A key contribution comes with G. Birkhoff who in 1957 discovered a principle for a uniform contraction of a (real) cone. This became a source of inspiration for me to develop a theory for complex cones, in particular implying a Perron-Frobenius like theorem for complex matrices.
Date Start: 26.04.2019, 10:00 Uhr
Ende: 26.04.2019 , 11:00 Uhr
Location Mathematisches Institut (Bunsenstr 3-5)
Hörsaal 4
Contact 0551-3927752