Learning Eigenvectors for Free Wouter M. Koolen Wojtek Kotłowski Manfred K. Warmuth Royal Holloway and CWI Centrum Wiskunde & Informatica UC Santa Cruz

We extend the classical problem of predicting a sequence of outcomes from a finite alphabet to the matrix domain. In this extension, the alphabet of n outcomes is replaced by the set of all dyads, i.e. outer products uu