Some question about inequation involoved trace?

This is a math question, not a CVX question. Nevertheless, …

I will assume X \succeq 0, but do no need to assume anything about rank(X)

Let M = H*X*H'. Then M is psd.

Therefore max(eig(M)) <= trace(M). Therefore (56) implies(57).

However, (57) does not imply(56).

ok,thanks, i have got it.