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 10:30–11:00, Auditorium Max Weber
Doubly stochastic matrices and the Bruhat order
Geir Dahl (University of Oslo)
Joint work with Richard A. Brualdi (University of Wisconsin), Eliseu Fritscher (Universidade Federal do Rio Grande do Sul)

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$. We introduce an extension of this, called the stochastic Bruhat order, for the larger class $\Omega_n$ of doubly stochastic matrices (i.e., nonnegative matrices with row and column sums 1). A characterization of this order is given, in terms of certain interchange operations. Moreover, several results on so-called Bruhat faces of $\Omega_n$ induced by permutation matrices, are given.