TITLE: When is a positive semi-definite matrix A positive definite?
QUESTION [6 upvotes]: 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.

REPLY [6 votes]: If the determinant of a positive semi-definite matrix is not zero (i.e., the matrix is non-singular), then it is positive definite. Because, determinant=Product of eigenvalues and a positive definite matrix have all positive (strictly greater than zero) eigenvalues.