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.