One of my homework solutions stated the following:
However, I do not seem to grasp why the solutions refers to 'both principal minors'. As far as I know there are three principal minors:
Order 1: det (2) = 2 and det (4) = 4
Order 2: det (2 12 ; 12 4) = -136
Wouldn't this mean that the Hessian matrix is NOT positive definite as the principal minor of order 2 is non-positive?
It might be important to show what f was defined as:
So my question now is whether the conclusion of the solution is correct: is the principal minor of order 2 not relevant to establish positive semi-definiteness?
Thank you very much in advance.