How to use variable Y in cvx

Nonconvex
1

if Y=vec(X)conj(transpose(X)) and X is a NN matrix.
sorry sir it is Y=vec(X)conj(transpose(vec(X))) and X is NN matrix.

2

This expression isn’t well posed. vec(X) is N^2\times 1, and conj(transpose(X)) is N\times N.