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This is a basic calculs/pre-calcuus question, that am having trouble with. For real matrices $A_{n \times n}$,$X_{n \times n}$ and $K_{n \times n}$ and a vector $c_{n \times 1}$, I want to have the derivative of the below function w.r.t the vector $c$ in a vector/matrix notation and not in terms of the individual entries of $c$. i.e the derivative w.r.t $c$ and not the derivative w.r.t each entry $c_i$. Note that $x_{i \mathbb{.}}$ denotes the row $i$ of $X$. I'd like to see a few steps in reasonable detail if you are re-arranging the below function in matrix notation! I also would like to have the second derivative w.r.t $c$.

The function is : $\sum_{i,j}A_{i,j}\left[\sum_{q=1}^nc_qK(x_{i\mathbb{.}},x_{q\mathbb{.}})-\sum_{l=1}^nc_lK(x_{j\mathbb{.}},x_{l\mathbb{.}})\right]^2$

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    Maybe if you write the expression in matricial form, it will be easier to work with.2012-10-24
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    Did you mean to write $\sum_{q=1}^n$ and $\sum_{\ell=1}^n$?2012-10-24
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    @littleO Yes! That is right.Edited and awaiting an answer.2012-10-24
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    @Pragabhava If I could represent this in a matrix form- I would not have posted this question. That is the reason-the differentiation seemed harder, to do in this form and get an answer in vector/matrix form2012-10-24
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    @qlinck The thing is that, for example, in the term under the square root looks like there is a dot product of vector $c$ with row $i$ of $K$, etc. Why don't you write a small example of what is $K$, $c$ and $A$ (i.e. $n = 2,\,3$).2012-10-24
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    @Pragabhava There is no square root. I believe you meant square. K,c and A are fixed matrices/vectors with real-entries. There are infinite examples to what real-numbers they can take. That said, yes-there indeed is an inner product(dot product).2012-10-24
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    @qlinck Sure, I meant square. I still don't understand the notation. Can you put a concrete example of $K$, $A$ and $c$, i.e. $K = \begin{pmatrix}\square & \square \\ \square & \square \end{pmatrix}$?2012-10-24
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    For clarification, what does $K(x_i, x_q)$ represent, exactly?2012-10-24
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    $K(x_i, x_q)$ can be viewed as the $i$, $q$ entry of a matrix $K$. $K(x_i, x_q)$ tells us that this scalar entry was formed by a function acting on the rows $x_i$, $x_q$ of $X$2012-10-24

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