# Non-Negative Vs Positive Semi Definite

A matrix is PSD if $$\langle Ax, x\rangle \ge 0, \forall x \in H$$

Where, H is a hilbert space and A is a mapping $$H \rightarrow H$$. Is it the same as being Non-negative? I couldn't seem to find a specific definition for a non-negative operator.

• Non-negative does not make much sense when talking about matrices. When saying non-negative , one is usually talking about real numbers, or integers – Pink Panther Mar 13 at 19:06
• I would say they are analogous, but the notion of non-negativity for a matrix doesn´t make much sense – Fede Poncio Mar 13 at 19:06