I'm little bit confused about the data matrices associated with an SDP program. Consider the following SDP program:
I know that the Matrix $X$ must be positive semidefinite i.e. $X \succeq 0$ as the last constraint implies. My question is about the data matrices $C$ and $A_i \forall i \in \{1, \cdots, m\}$. Do they have to be positive semidefinite ? In other words, can we have a matrix $C$ for example that is either negative definite or indefinite ?