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I have a symmetric matrix whose diagonals are positive. I need to prove that this matrix is positive semidefinite.

The matrix is made up of a bunch of constants and I tried getting the eigenvalues using Maple and it was a mess. I also tried doing something I found online How to check if a symmetric $4\times4$ matrix is positive semi-definite?. I tried doing Robert Israel's answer and it ended up being a mess. Is there an easier way to prove positive semidefinite?

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  • $\begingroup$ How large is your matrix? Perhaps you can post it here. I would venture to guess that you may be able to apply the Gershgorin Circle Theorem. This is noted in Calle's answer in the question you linked to. $\endgroup$ – EuYu Nov 28 '12 at 4:21
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    $\begingroup$ Symmetric matrices with positive diagonals aren't always positive. (E.g., $\begin{bmatrix}1&2\\2&1\end{bmatrix}$.) What is your matrix? $\endgroup$ – Jonas Meyer Nov 28 '12 at 4:21
  • $\begingroup$ If your matrix is not too large, see this : math.stackexchange.com/questions/40849/… $\endgroup$ – Bhargav Nov 28 '12 at 4:22
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    $\begingroup$ @b555: That is the question user972276 links to above. $\endgroup$ – Jonas Meyer Nov 28 '12 at 4:23
  • $\begingroup$ oops my bad, sry .. had read the q i linked just a few days abck and couldnt read this q fully >.< $\endgroup$ – Bhargav Nov 28 '12 at 4:26
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How large is your matrix? Perhaps you can post it here. I would venture to guess that you may be able to apply the Gershgorin Circle Theorem. This is noted in Calle's answer in the question you linked to.

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