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Short question:

How can I calculate $\dfrac{\partial A}{\partial L}$ where $A = \|Lx\|^2_2= x^TL^TLx$?

Is it $\dfrac{\partial A}{\partial L}=2Lx^tx$?

Long question:

I want to calculate the gradient of a Mahalanobis distance. More specifically, I like to calculate the gradient of $A$ in terms of $L$, ($\frac{\partial A}{\partial L}$).

$$A = \|Lx\|^2_2= x^TL^TLx$$

I expand the equation and calculate the gradient element by element and it seems it should be something like $\frac{\partial A}{\partial L}=2Lx^tx$. But, it's very slow! Would you please confirm the correctness of answer? and help me find a faster approach?

Thanks

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    Hint to check your solution: what happens when L is a scalar?2012-03-22

4 Answers 4