The matrices $A$, $C$, and $R$ have dimensions $m\times n$, $m\times k$ and $k\times n$. Set $E= \left \| A- CR \right \|_{2}^{F}= \sum_{r= 1}^{m}\sum_{s= 1}^{n}\left \{ \left ( A- CR \right )_{rs} \right \}^{2}$. Show that $\frac{\partial E}{\partial C}= 2\left ( CR- A \right )R^{T}$ and $\frac{\partial E}{\partial R}= 2C^{T}\left ( CR- A \right )$.
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