How do you differentiate the following expressions with respect to the vector $x$.
I think I might be a little conceptually confused on what happens when you take the derivative with respect to a vector. What dimensions should you end with? For the problem, I am trying to solve, I think I should end up for each of these derivatives with the results in the derivative to be $R^{1\times1}$.
$\frac{d}{dx}(b^TAx)$
$\frac{d}{dx}(x^TAb)$
$\frac{d}{dx}(x^TAx)$
where $b, x \in R^{n\times 1}$ and $A \in R^{n\times n}$
Also, if it helps A for this case is symmetric.
Update:
Thanks to the extra motivation by Mike and joriki, I think I now have them solved.
$\frac{d}{dx}(b^TAx) = Ab$
$\frac{d}{dx}(x^TAb) = Ab$
$\frac{d}{dx}(x^TAx) = \textbf{A}\textbf{x} + \textbf{A}^T\textbf{x}$
But if anyone, would like to double check it that would be great.