# study the differentiability of this function

Let $A$ be a square matrix of size $n^2$ over $\mathbb R$, i.e $A\in M_{nn}(\mathbb R)$. Define the function $h:\mathbb R^n \to \mathbb R^n$ defined by $h(x)=x^tAx$.

How can I find the cases in which $h$ is a differentiable function?

• I think, you have $h:R^{n}\rightarrow R$...$h$ is a quadratic function and hence differentiable...where is the problem? – Alex May 11 '13 at 17:31
• @Trafalgaw If $x$ is $n\times 1$, then $x^TAX$ is $1\times 1$, therefore the codomain of $h$ should be $\Bbb R$. – Git Gud May 11 '13 at 17:31
• You are right, Thanks! – Trafalgaw May 11 '13 at 17:42
• @Trafalgaw You can edit the question. – Git Gud May 11 '13 at 17:44