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SUMMARY:Cordelia Li (William & Mary)
DTSTART:20210929T180000Z
DTEND:20210929T190000Z
DTSTAMP:20260423T005816Z
UID:WMGAG/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WMGAG/11/">C
 opositive matrices\, their dual\, and the Recognition Problem</a>\nby Cord
 elia Li (William & Mary) as part of GAG seminar\n\nLecture held in Jones H
 all 302.\n\nAbstract\nCopositivity is a generalization of positive semidef
 initeness.  It has applications in economics\, operations research\, and s
 tatistics.\nAn $n$-by-$n$ real matrix $A$ is copositive (CoP) if $x^TAx \\
 ge 0$ for any nonnegative vector $x \\ge 0$.  The CoP matrices form a prop
 er cone.\nA CoP matrix is ordinary if it can be written as the sum of a po
 sitive semidefinite (PSD) matrix and a symmetric nonnegative (sN) matrix.\
 nWhen $n < 5$\, all copositive matrices are ordinary.  However\, recogniti
 on that a given CoP matrix is ordinary and the determination of an ordinar
 y decomposition is an unresolved issue.\nHere\, we make observations about
  CoP-preserving operations\, make progress about the recognition problem\,
  and discuss the relationship between the recognition problem and the PSD 
 completion problem.\nWe also mention the problem of copositive spectra and
  its relation to the symmetric nonnegative inverse eigenvalue problem.\n
LOCATION:https://researchseminars.org/talk/WMGAG/11/
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