I read in Lovasz's notes about semidefinite programs and combinatoric optimization.
If $x_1A_1 + ... + x_nA_n\succ 0$ has no solution, then the linear subspace $L = x_1A_1 + ... + x_nA_n$ is disjoint from the interior of the PSD cone. It follows that this linear space is contained in a hyperplane that is disjoint from the interior of the PSD cone. I think this is related to the hyperplane separation theorem. How is this statement related to the hyperplane theorem and why it is true?
