I'd like to know how to prove the following:

If A is a symmetric matrix, show that A is positive definite if and only if its eigenvalues are positive.

Thanks!!

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- March 16th 2009, 11:06 AMborrachoProof: positive definite and positive eigenvalues
I'd like to know how to prove the following:

If A is a symmetric matrix, show that A is positive definite if and only if its eigenvalues are positive.

Thanks!!