# When is a positive semi-definite matrix A positive definite?

Does it has something to do with the determinant of A? I saw two seperate websites - one which claims that when the determinant of A is zero, and the other claims that when the determinant of A is not zero, then the positive semi-definite matrix is positive definite.

Can someone explain to me which is the correct answer, and the reason behind it? Thank you.

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take a look: en.wikipedia.org/wiki/Sylvester's_criterion – Ilya Oct 12 '11 at 20:50