I am having problems with implementing back propagation of this...

Let $O,P \in R^{K \times K}$ and $x \in R^K$.

I have this operation $$y:= OPx$$

How can I find $\frac{\partial y}{\partial P}$?

If I decompose $y$ into: $$q := Px$$ $$y := Oq$$

I know that $$\frac{\partial y}{\partial P} = \frac{\partial y}{\partial q} \frac{\partial q}{\partial P}$$ and $$\frac{\partial q}{\partial p} = x$$ but by trial and error I know that $$\frac{\partial y}{\partial q} \neq O$$

So how can I solve the optimization for $P$?

Thank you for reading!


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