I have this introductory problem:
Calculate the gradient:
$$ \nabla_x \boldsymbol{a}^T \boldsymbol{x} = \boldsymbol{a} $$
$\boldsymbol{a}$ and $\boldsymbol{x}$ are vectors.
There are several things that were confusing to me in this exercise. First, I had trouble understanding the notation $\nabla_x$ i.e. what is gradient with superscript $x$ supposed to mean but according to this answer it is a vector of variables with respect to which you calculate the partial derivatives. Second thing is the presence of the right hand side of the equation - at first I thought it's like solving an unknown in e.g. $5+4x=16$. But now I'm convinced the RHS is just the answer I'm supposed to get by evaluating LHS.
I still don't how I should think about the question asking me to calculate gradient of what evaluates to be a vector - according to the Gradient wikipedia page you calculate gradient of a function, not a vector like here. Does it have some special meaning?
Edit: I just realized the matrix resulting from $\boldsymbol{a}^T \boldsymbol{x}$ is a 1x1 matrix, so if I treat it as just an expression it makes more sense.