Taking derivative of a function

Question

I have function and need to take partial derivatives respect to its two variables.

The function is:

Since I am not really good at math, I need some help to know the following derivatives:

Vectors? What is the transposed of p(i)? This is unusual notation. — Erwin Kalvelagen, Jan 30 '18 at 14:02
I'm voting to close this question as off-topic because it is about [math.se] instead of programming or software development. — Pang, Feb 15 '18 at 02:26

score 1 · Accepted Answer · answered Jan 30 '18 at 18:30

1

Let F(p,q) be

F(p,q) = sum(j, [ r(j) - sum(i, p(i,j)*q(i,j)) ]^2 )

Then dF/dp is the matrix A formed by elements

A(i,j) = 2 * [r(j) - sum(k, p(k,j)*q(k,j))] * (-q(i,j))

dF/dq is the matrix B formed by elements

B(i,j) = 2 * [r(j) - sum(k, p(k,j)*q(k,j))] * (-p(i,j))

answered Jan 30 '18 at 18:30

Erwin Kalvelagen

Thanks for your reply. What is the index k? – mgokhanbakal Jan 30 '18 at 19:18
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That is just a name. You can use another name. (Note: We cannot use `i` there because that is already used to index A(i,j) or B(i,j)) – Erwin Kalvelagen Jan 30 '18 at 19:50

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