Is there a name or notation for the diagonal matrix of partial derivatives?
If I have a vectors $x = \begin{bmatrix}x_1 & \dotsc & x_n \end{bmatrix}^T$, and $y = \begin{bmatrix}y_1 & \dotsc & y_n \end{bmatrix}^T$, and I want the vector of partial derivatives, what's the unambiguous way to write that? If I say $\nabla_x y$, that's the matrix of gradients. If I say $\nabla_x \cdot y$, that's the trace of the matrix. I want ${\mathrm{diag}}(\nabla_x y)$ or ${\mathrm{diag}}(\nabla_x) y$. How should write this?