In my lecture notes it says that:
The set $\mathcal{Q}$ of all quadratic forms on $\Bbb R^n $ is a subspace of the vector space V of all functions $f : \mathbb{R}^n → \mathbb{R}.$ (Recall that there is a one-to-one correspondence between quadratic forms and symmetric matrices.)
I was just curious how one would go about showing this? I.e., closure under addition, scalar multiplication and non-emptiness?
I think if someone can show me closure under either addition or scalar multiplication, I can figure out the rest, but I'm just stuck trying to start on this.