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DESCRIPTION: Matrices of nonnegative rank at most r form a semialgebraic se
 t. This semialgebraic set is understood for r=1\,2\,3. In this talk\, I wil
 l recall what was previously known about this semialgebraic set and present
  recent results on the boundaries of the set of matrices of nonnegative ran
 k at most four using notions from the rigidity theory of frameworks. These 
 results are joint work with Robert Krone. In the nonnegative rank three cas
 e\, all boundaries are trivial or consist of matrices that have only infini
 tesimally rigid factorizations. For arbitrary nonnegative rank\, we give a 
 necessary condition on zero entries of a nonnegative factorization for the 
 factorization to be infinitesimally rigid\, and we show that in the case of
  5×5 matrices of nonnegative rank four\, there exists an infinitesimally ri
 gid realization for every zero pattern that satisfies this necessary condit
 ion. However\, the nonnegative rank four case is much more complicated than
  the nonnegative rank three case\, and there exist matrices on the boundary
  that have factorizations that are not infinitesimally rigid. We discuss tw
 o such examples. 
DTSTAMP:20190304T153900
DTSTART:20190415T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Kaie Kubjas (Sorbonne Université Paris): Nonnegative rank four boun
 daries
UID:95690513@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190415-L-Kubjas.html
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