I'm stuck in a problem on positive definite matrices. I should show that "if all eigenvalues of A are positive, then A >= 0."
EDIT: assuming A is diagnosable.
I know the definition for a positive definite matrix is that x'Ax >= 0 for all x (but does "x" herein refer to the eigenvectors?). I've spent many hours on trying to figure this out, but I don't really grasp the idea of how to get started here..
Would greatly appreciate help!!