A concise formula for the Hessian determinant of a function parameterising a quadratic hypersurface

Abstract

We will give a concise formula for the Hessian determinant of a smooth function $y:{\mathbb{R}}^n\supseteq \Omega \to \mathbb{R}$ such that its graph is contained in a quadratic hypersurface. The proof will make heavy use of matrix algebra.