I have a problem about the derivation of sum squared vector when I study a paper. The confusion isenter image description here
We just take the first section of the $f(\zeta$) as an example. Both $\gamma$ and $\zeta$ are 1xM vectors. From the paper, it seems to use the calculation result that for $f(\zeta) = (\zeta\gamma)^2$, the result of $\nabla f(\zeta) = 2\zeta\gamma^2$. However, I do not think this is the correct answer, since if we assume the length of vectors are just 2 and expand the equation,
$f(\zeta) = (\zeta_1\gamma_1 + \zeta_2\gamma_2)^2 = \zeta_1^2\gamma_1^2 + \zeta_2^2\gamma_2^2 + 2\zeta_1\zeta_2\gamma_1\gamma_2$, differentiate the function with $\zeta = [\zeta_1$ $\zeta_2]$,
we get $\nabla f(\zeta) = 2\zeta_1\gamma_1^2 + 2\zeta_2\gamma_2^2 + 2\gamma_1\gamma_2 = 2\zeta\gamma^2 + 2\gamma$. And it is obviously that the same same the $\nabla f(\zeta) = 2\zeta\gamma^2$ calculation given in the paper above.
I do not know if that's because my calculation of vector derivation processing is wrong or I missed something. Please tell me how to do with the correct way of derivation within the vectors. Thank you!