Let's play around with matrix derivatives! A trace Tr(X) of a matrix X is a sum of its diagonal elements. For example: ![\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%26amp%3B3%5C%5C4%26amp%3B5%26amp%3B6%5C%5C7%26amp%3B8%26amp%3B9%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]")
trace(X)=1+5+9=15. Note that trace is a scalar! Let's find a matrix notation for \frac{\partial Tr(X^2)}{\partial X} ∂X ∂Tr(X 2 ) for matrix X = \left( \right)X=( x 1,1 x 2,1 x 1,2 x 2,2 ), where X^2X 2 is a matrix product X \cdot XX⋅X. Please do this element-wise and figure out a matrix notation for it:
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2X.T
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