Paper, B.2. Proof of Lemma 4.1 - σ

[ndvbd]

In the proof, I don't see the definition of σ. Is it defined in the lemma? In the deriviation of L(Q,B∗)?

2. If you can explain in Theorem 4.3 how you used the Von Neumann trace inequality that would be lovely. I think it is an equality and not an inequality there, because you inserted $Q^TQ$ which is Identity, since Q is orthogonal, so the whole expression is equal IMHO

3. Why E[III_B] has the term (r/d) in it? since the trace is cyclic invariant, I think we can get rid of UU^T and then there's no (r/d) term