Suppose
\begin{align} y&=Ax\\ z&=f(y) \end{align}
Then, is it true that: \begin{align} \nabla_xz&=\nabla_yf(y)\nabla_xy \\ &=\nabla_yf(y)A \end{align}
Dimensions:
- $A: m \times n$
- $x: n \times 1$
- $y: m \times 1$
- $z: 1 \times 1$
- $\nabla_yf(y): 1 \times m$?
- $\nabla_xz: 1 \times n$?