# If eigenvalues of a symmetric matrix are positive, is the matrix positive definite?

If eigenvalues of a symmetric matrix are positive, does that mean it is positive definite? please give an example of why this is incorrect.

• What are you using as the definition of "positive definite"? Are you considering complex matrices that are symmetric but not hermitian? – Robert Israel Feb 18 '16 at 19:18

The symmetric (but not hermitian) matrix $$\pmatrix{2 & i\cr i & 0\cr}$$ has $1$ as its only eigenvalue, but it is not positive definite.