if Hessian matrix of a function has positive real eigenvalues, then function is positive definite Can we say that if Hessian matrix of a function has positive real eigenvalues, then function is positive definite? Is it true? Would you recommend a document for me to read on this subject?
$V=\alpha x^2+\alpha y^2+ z^2$, I know this function is positive definite for $\alpha >0$. But I wonder if it would be correct to check with its Hessian matrix as I asked above?

There are simple counterexamples, such as $V(x,y)=x+x^2+y^2$, which is obviously not positive definite although its Hessian has eigenvalues $\lambda_1=\lambda_2=2$.
