Some equivalent transform about trace?

[jifazhang]

If rank(X)>1 or X is full rank, can we have similar equivalent transmfrom like below two equations?

[jifazhang]

thank you, in my problem, X is a PSD matrix, which needs to be optimized. I think i can not perform matrix decomposition of it.

[jifazhang]

ok, thank you.
i want to tackle the robust constraint 42b,where w is the optimization problem.

[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).

[jifazhang]

ok，thank you, i think i should read some linear algebra relared books to tackle my problem.