Bárány Imre (Rényi Intézet): A matrix version of Steinitz’s lemma

Steinitz's lemma is about a finite set V of at most unit vectors in R^d whose sum equals zero. It states that the elements of V can be ordered so that all partial sums along this ordering have norm at most 2d. The lemma has many applications in various parts of mathematics. I plan to explain some of them, and I'm going to state and prove a matrix version of this lemma.