For this problem it's given that $Q\in \mathbb{R}^{n\times n}$ is positive semi-definite, and now I'm trying to figure out whether $$g(x) = \sqrt{x^TQx-1}$$ is convex over $\mathbb{R}^n$
I did a similar problem where the $-1$ in the function was just replaced with a $+1$, and I found that that function was convex. Using similar methods, I've been unable to show whether g is convex, let alone strictly convex.
Any suggestions about methods to use here would be much appreciated. Thank you!