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SUMMARY:Alexander Belton (Department of Mathematics and Statistics\, Lanca
 ster University\, UK)
DTSTART:20200722T130000Z
DTEND:20200722T140000Z
DTSTAMP:20260423T024424Z
UID:PortMATHS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PortMATHS/7/
 ">Preservers for positive-semidefinite and totally positive matrices</a>\n
 by Alexander Belton (Department of Mathematics and Statistics\, Lancaster 
 University\, UK) as part of Portsea Maths Research Webinar\n\n\nAbstract\n
 The Schur product theorem implies that the set of positive-semidefinite ma
 trices is invariant under the entrywise application of any absolutely mono
 tonic function. Shoenberg's work shows that the converse is also true: a f
 unction which preserves positive semidefiniteness for matrices of arbitrar
 y size is necessarily absolutely monotonic. For totally positive matrices\
 , the class of preservers is much smaller\, being only the linear homothet
 ies.\n\nThe situation is more complex for matrices of a fixed size\, or wh
 en the class of matrices under study has some additional structure. This t
 alk will address these questions\, including the cases of Hankel and Toepl
 itz matrices.\n\nThis is joint work with Dominique Guillot (University of 
 Delaware)\, Apoorva Khare (Indian Institute of Science\, Bangalore) and Mi
 hai Putinar (University of California at Santa Barbara and Newcastle Unive
 rsity).\n
LOCATION:https://researchseminars.org/talk/PortMATHS/7/
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