We will discuss some connections between classical topics in matrix theory and some modern problems in quantum information. We will show a relationship between the Bures angle in quantum information and the canonical angles between subspaces. We show how the answer to a Putnam competition problem on Hadamard matrices can be used to find the order of all maximal Abelian subgroups of tensor products of the Pauli matrices. A connection between the Hadamard matrix conjecture and Operator systems will also be discussed.

Parts of this talk are joint work with one of more of: J.Li, S. Plosker, J. Levick, T. Jochym-O’Connor, D.W. Kribs and R. Laflamme.