Preservers for positive-semidefinite and totally positive matrices
Alexander Belton (Department of Mathematics and Statistics, Lancaster University, UK)
Abstract: The Schur product theorem implies that the set of positive-semidefinite matrices is invariant under the entrywise application of any absolutely monotonic function. Shoenberg's work shows that the converse is also true: a function which preserves positive semidefiniteness for matrices of arbitrary size is necessarily absolutely monotonic. For totally positive matrices, the class of preservers is much smaller, being only the linear homotheties.
The situation is more complex for matrices of a fixed size, or when the class of matrices under study has some additional structure. This talk will address these questions, including the cases of Hankel and Toeplitz matrices.
This is joint work with Dominique Guillot (University of Delaware), Apoorva Khare (Indian Institute of Science, Bangalore) and Mihai Putinar (University of California at Santa Barbara and Newcastle University).
general mathematics
Audience: researchers in the topic
( slides )
Portsea Maths Research Webinar
Series comments: The theme for June is "Probability theory and related fields". The theme for July is "Linear algebra and its applications". There are no webinars in August.
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