Let $A$ be a symmetric $n\times n$ matrix with entries only 0 or 1 and the diagonal entries of $A$ are all 1. Is A positive (semi-) definite?




  • $\begingroup$ Its all eigenvalues are 1 $\endgroup$ – Shailesh Feb 17 '15 at 10:14
  • 1
    $\begingroup$ @Shailesh No, they aren't. But you don't really need the eigenvalues: what about calculating the matrix principal minors? $\endgroup$ – Timbuc Feb 17 '15 at 10:15
  • $\begingroup$ The trace is $3$, the determinant is $-1$. $\endgroup$ – Git Gud Feb 17 '15 at 10:16
  • $\begingroup$ sorry, I made a mistake in calculation. $\endgroup$ – Shailesh Feb 17 '15 at 10:20

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