What's the derivative of $f(w)$ with respect to the vector $w$?
$f(w)=\mathrm{tr}(ww'A) + x^{\prime}ww'x$
Note:
$x,w$ are vectors and $A$ is a square matrix.
${}'$ indicates transpose
Thanks.
What's the derivative of $f(w)$ with respect to the vector $w$?
$f(w)=\mathrm{tr}(ww'A) + x^{\prime}ww'x$
Note:
$x,w$ are vectors and $A$ is a square matrix.
${}'$ indicates transpose
Thanks.
It is usually good to write it out explicitly in coordinates. As far as I understand your notation, you have $f(w) = \sum_{ij} w_i w_j A_{ji} + \sum_{ij} x_i w_i w_j x_j.$
Taking the derivative with respect to $w_k$, we have $\frac{\partial f(w)}{\partial w_k} = \sum_j[ w_j (A_{jk} + A_{kj}) + 2 x_k w_j x_j] .$