1
$\begingroup$

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?

$\endgroup$
2
$\begingroup$

Hint:

$$\begin{pmatrix}1&0&1\\0&1&1\\1&1&1\end{pmatrix}$$

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.