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.

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

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