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dc.contributor.authorBelton, Alexander
dc.contributor.authorGuillot, D
dc.contributor.authorKhare, A
dc.contributor.authorPutinar, M
dc.date.accessioned2023-02-13T10:21:06Z
dc.date.available2023-02-13T10:21:06Z
dc.date.issued2020
dc.identifier.issn0271-4132
dc.identifier.issn1098-3627
dc.identifier.urihttp://hdl.handle.net/10026.1/20268
dc.description.abstract

This survey contains a selection of topics unified by the concept of positive semidefiniteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). We put emphasis on entrywise operations which preserve positivity, in a variety of guises. Techniques from harmonic analysis, function theory, operator theory, statistics, combinatorics, and group representations are invoked. Some partially forgotten classical roots in metric geometry and distance transforms are presented with comments and full bibliographical references. Modern applications to high-dimensional covariance estimation and regularization are included.

dc.format.extent109-150
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectmetric geometry
dc.subjectpositive semidefinite matrix
dc.subjectToeplitz matrix
dc.subjectHankel matrix
dc.subjectpositive definite function
dc.subjectcompletely monotone functions
dc.subjectabsolutely monotonic functions
dc.subjectentrywise calculus
dc.subjectgeneralized Vandermonde matrix
dc.subjectSchur polynomials
dc.subjectsymmetric function
dc.subjectidentities
dc.subjecttotally positive matrices
dc.subjecttotally non-negative matrices
dc.subjecttotally positive completion problem
dc.subjectsample covariance
dc.subjectcovariance estimation
dc.subjecthard / soft thresholding
dc.subjectsparsity pattern
dc.subjectcritical exponent of a graph
dc.subjectchordal graph
dc.subjectLoewner monotonicity
dc.subjectconvexity
dc.subjectand super-additivity
dc.titleA panorama of positivity. II: Fixed dimension
dc.typeconference
dc.typeChapter
plymouth.author-urlhttps://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000564770600005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=11bb513d99f797142bcfeffcc58ea008
plymouth.volume743
plymouth.publication-statusPublished
plymouth.journalComplex Analysis and Spectral Theory
dc.identifier.doi10.1090/conm/743/14958
plymouth.organisational-group/Plymouth
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering
plymouth.organisational-group/Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics
plymouth.organisational-group/Plymouth/Users by role
plymouth.organisational-group/Plymouth/Users by role/Academics
dcterms.dateAccepted2019-05-19
dc.rights.embargodate2023-2-25
dc.identifier.eissn1098-3627
dc.rights.embargoperiodNot known
rioxxterms.versionofrecord10.1090/conm/743/14958
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
rioxxterms.typeJournal Article/Review


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