Some equivalent transform about trace?

[jackfsuia (Jack)]

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).