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Math notation confusion Sat 22 Aug 21:02:15 2020 No.12036869 View Reply Original Report

Quoted By: >>12036922

In the pic I posted with this thread I am confused how they jump from the sum k = 1 to n ?u/?yk ?yk/?xi to ?u/?uyk*(Oki) how do they replace part of the partials with the matrix Oki?

Math notation confusion

Math notation confusion Sat 22 Aug 2020 21:15:44 No.12036907 Report

Quoted By: >>12036922

I notice that only the row is varying and it's stays in the second column. I see now it's because everywhere else the matrix would go to zero. Is that how they make that substitution? so the derivative of v with respect to x2 I would get Ok2 where only the k varies, which is the row. Column 2 is fixed because it contains the x2 variable, all other partials are going to zero since they are held constant.

Anonymous

Anonymous Sat 22 Aug 2020 21:26:43 No.12036922 Report

Quoted By: >>12036955

>>12036869
>>12036907
they're just replacing $\frac{\partial y_k}{\partial x_i}\rightarrow o_{ki}$ because of the definition $y_k=\sum_i o_{ki}*x_i$ in line 2. It seems your confusion stems from your understanding of this 2nd line.

I changed some of the summation indices from line 2 to make it easier to see

Math notation confusion

Math notation confusion Sat 22 Aug 2020 21:41:23 No.12036955 Report

Quoted By: >>12036959 >>12036972

>>12036922
I kind of half get it. How do you make that substitution from that definition though? I get that the column is fixed and the row varies giving you essentially a dot product. but I still dont get how you can subtitute a partial derivative for a matrix element.

Anonymous

Anonymous Sat 22 Aug 2020 21:44:17 No.12036959 Report

Quoted By: >>12037034 >>12037039

>>12036955
look at the two equations I wrote out for you in my post above. take $\frac{\partial y_k}{\partial x_i}$ from the definition of $y_k$ . What are you left with?

If that still doesn't make sense, write out an explicit representation of $y_k$ in just 3 dimensions, including every term (instead of the summation). That should help.

Anonymous

Anonymous Sat 22 Aug 2020 21:50:43 No.12036972 Report

Quoted By:

>>12036955
maybe you're confused about the fact that matrix elements are just numbers?

Math notation confusion

Math notation confusion Sat 22 Aug 2020 22:19:31 No.12037034 Report

Quoted By: >>12037069

>>12036959
...So take the partial of yk with respect to xk...That's going to give you 0's for a lot of matrix entries, correct. You are basically getting rid of every part of the linear combination except the xk partial.

Math notation confusion

Math notation confusion Sat 22 Aug 2020 22:22:22 No.12037039 Report

Quoted By: >>12037069

>>12036959
Oh shit. so inside the summation I get oki (?yk(xi)/?xi) and (?yk(xi)/?x1) = 1! Is that correct?

Anonymous

Anonymous Sat 22 Aug 2020 22:35:42 No.12037069 Report

Quoted By: >>12037093

>>12037034
it will get 0 for every single matrix entry except for one, corresponding to the x you're differentiating wrt. yes.
>>12037039
I'm not sure what this means. taking the derivative should yield the oki that is the coefficient of the xi

Math notation confusion

Math notation confusion Sat 22 Aug 2020 22:46:08 No.12037093 Report

Quoted By:

>>12037069

What I mean is that if I take the partial ?yk/?xi
inside the summation symbol I would have:
Oki*?(xi)/?xi which gives me = Oki, right?

Math notation confusion

Math notation confusion Sat 22 Aug 2020 22:49:57 No.12037096 Report

Quoted By:

I understand that part now. I am required to take the derivative of v(x) again, and it gets a little confusing. I think i'll post another thread on the subject.

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