After some search here and on Google, I couldn't find a way to determine the definiteness of this matrix:
My understanding is that it should be negative semi-definite since all principal minors are $\leq 0$.
However, in the sample solutions of the book I am working through it stated that it is neither positive nor negative semi-definite.
A general procedure (for positive and negative semi-definiteness) would be really helpful.
Why is that?