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What are the conditions for a binary matrix $A$ (matrix with elements 0 or 1) to be positive definite (not even symmetric), i.e.

$\forall x\neq 0, x^TAx>0, A_{ij}\in \{0,1 \}$

Put it another way, what adjacency matrices are positive definite?

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    How about positive semi-definite relations? Is there any reflexive, transitive, and nonsymmetric relation, which is PSD?2012-09-19

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