I'm learning that if $n \times n$ positive definite matrix A A's then $\forall v$ $v^TAv>0 \ $, but this requires A is symmetric(then A have orthonormal eigenvectors)
so I'm asking:
1.if A is not symmetric, but still have n eigenvectors with n positive eigenvalues, would $v^TAv>0 \ $ forall $v$
2.if A have r eigenvectors (r<n) with r eigenvalues, but all of them are positive, would $v^TAv>0 \ $ forall $v$
