How to deal with quadratic constraint in semidefinite programming

I am using CVX to solve an optimization problem. One of my constraints in the problem is: M \succeq \eta {\eta}^T, where M is a square matrix and \eta is a column vector (both M and \eta are variables). But CVX issues an error said “Only scalar quadratic forms can be specified in CVX”. I think the error results from the quadratic form of the constraint. I am wondering if I can convert the constraint into another equivalent form?

Your question has been answered by Johan Lofberg at . That formulation approach can be straightforwardly implemented in CVX.