ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Nonnegative Matrices and Majorization

Wed 11:30–12:00, Auditorium Max Weber
Zero-one completely positive matrices and the $\mathcal A(R,S)$ matrix classes
Torkel Andreas Haufmann (University of Oslo)
Joint work with Geir Dahl (University of Oslo)

A matrix $A$ is completely positive if it has a factorization $A = BB^T$ where $B$ is a nonnegative matrix. The class of completely positive matrices has attracted a great deal of study.

Berman and Xu (2005, 2007) introduced the related notion of $\{0,1\}$-completely positive matrices: A matrix $A$ is $\{0,1\}$-completely positive if it has a factorization $A = BB^T$ where $B$ is a $(0,1)$-matrix. In the first part of this talk we discuss a connection between the $\{0,1\}$-completely positive matrices and the correlation cone, and show that this link casts the results of Berman and Xu in a new light, as well as allowing some extensions of these previous results.

In the second part of the talk we discuss the $\{0,1\}$-completely positive matrices as the image of the classes $\mathcal A(R,S)$ of $(0,1)$-matrices with prescribed row and column sums. The goal is to obtain results on the cardinality of $f(\mathcal A(R,S))$, where $f$ is the function $X \mapsto XX^T$.