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?

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

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