FB 6 Mathematik/Informatik

Institut für Mathematik


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WS 2017/18

21.11.2017 um 17:15 Uhr in Raum 69/117

Dr. Mateusz Michalek (MPI Leipzig)

Algebra, Geometry and Fast Matrix Multiplication

29.11.2017 um 17:15 Uhr in Raum 69/125

Kaie Kubjas (Aalto University, Finland)

Geometry of Nonnegative and Positive Semidefinite Rank

One of many definitions gives the rank of an mxn matrix M as the smallest natural number r such that M can be factorized as AB, where A and B are mxr and rxn matrices respectively.
In many applications, we are interested in factorizations of a particular form. For example, factorizations with nonnegative entries define the nonnegative rank and are closely related to mixture models in statistics.
Another rank I will consider in my talk is the positive semidefinite (psd) rank. Both nonnegative and psd rank also appear in optimization and complexity theory.
Nonnegative and psd rank have geometric characterizations using nested polytopes.
I will explain how to use these characterizations to study the semialgebraic geometry of the set of matrices of given nonnegative or psd rank.