I have a symmetric matrix where the diagonals are all positive. I need to prove the 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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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.