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June 19th, 2016, 11:52 AM   #1
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Help with vector based issue

Hello all!

Firstly, I apologize for my lack of knowledge in this field, I'm struggling with what I'm sure is a simple issue, but it's beyond me right now.

Ok so.. I'm trying to figure out the "weight" of a set of vectors that are added together to form a "final" vector.

For example:
vector1 = (5,5)
vector2 = (-6,5)
vector3 = (3,5)

finalVector = vector1 + vector2 + vector3

How would I workout the "weight" (normalized 0-1) that vector2 has on the finalVector position?


Thank you for any help you can give.

Mike.
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June 19th, 2016, 01:53 PM   #2
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"weight" is undefined in this context. It could mean length or length squared.
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June 21st, 2016, 01:31 PM   #3
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Thank you for the reply mathman.

Ah ok, I understand.

If finalVector is the full movement of a 2d point from (0,0) to finalVector. Is there a way to find out "how much" or the "percentage" of the finalVector movement that each vector contributes?
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June 21st, 2016, 04:52 PM   #4
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You still need a precise definition of weight.
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June 22nd, 2016, 04:12 AM   #5
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$\displaystyle v_1=(5,5),v_2=(-6,5),v_3=(3,5)$
The normal defined vector sum is $\displaystyle v_1+v_2+v_3=(2,15)$
This kind of sum may cause data lose of "weight" by some means
You can't normalize it to 0-1 with this vector sum

Think of defining it with normalizing it to 0-1
https://en.wikipedia.org/wiki/Norm_(mathematics)
use 1-norm to define "weight" for each vector
$\displaystyle ||v_1||_1=10,||v_2||_1=11,||v_3||_1=8$
$\displaystyle ||v_1||_1+||v_2||_1+||v_3||_1=29$
$\displaystyle weight(v_1)=\frac{10}{29},weight(v_2)=\frac{11}{29 },weight(v_3)=\frac{8}{29}$
Generally,$\displaystyle weight(v_i,p)=\frac{||v_i||_p}{\sum_i ||v_i||_p}$
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June 22nd, 2016, 12:43 PM   #6
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Thank you for the replies, mathman, fungarwai.

fungarwai! Thank you so much for the detailed reply.

This is a big, big help in solving my problem. It's almost there, the only issue I have is a slight data loss in "weight" that I'm getting from this method, that you mentioned.

Is there any way around this? Any topics I can study to guide me in the right direction to something that will help?

Thanks again.
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June 23rd, 2016, 03:42 AM   #7
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I learn these from lessons about matrix

May called linear algebra, functional analysis as wikipedia mentioned
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