Critical points of a nonnegative quadratic form on a subspace

Question

Let $Q(x)=x^tAx$ for some square symmetric matrix $A\in R^{n\times n}$, such that $Q(x)\geq0$ for each $x\in R^n$. Let $S$ be an affine subspace of $R^n$. How can I show that if $y$ is a critical point of $Q$ on $S$, then $y$ is a point of global minimum of $Q$ on $S$?

Answer 1

Notice that you have a strictly convex function in the subspace.