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Old 11-27-2013, 06:51 AM
blunderboy blunderboy is offline
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Lightbulb Point Xj is linear combination of rest of the other points ?

I remember in lecture 7, professor used a property

For any d+2 points, we can write

Xj as linear combination of rest of the points.

Q1. What is the proof for this property ?

Let us take an example: d = 1 and points are (5,10,7)
Q2. How do we write 7 in terms of 5 and 10 ?
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Old 11-27-2013, 03:27 PM
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yaser yaser is offline
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Default Re: Point Xj is linear combination of rest of the other points ?

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Originally Posted by blunderboy View Post
I remember in lecture 7, professor used a property

For any d+2 points, we can write

Xj as linear combination of rest of the points.

Q1. What is the proof for this property ?

Let us take an example: d = 1 and points are (5,10,7)
Q2. How do we write 7 in terms of 5 and 10 ?
Take a look at http://en.wikipedia.org/wiki/Linear_independence

For d=1, the vectors are two-dimensional (d+1) because of the zeroth coordinate, but to answer your specific question, 7=a_1 \times 5 + a_2 \times 10 has many solutions, for instance, a_1=0.4 and a_2=0.5.
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Old 11-27-2013, 09:36 PM
blunderboy blunderboy is offline
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Default Re: Point Xj is linear combination of rest of the other points ?

Thank you professor..I was under impression we have to take only integer values for Ai. I will go through the linear independence once from wiki. Thanks for the link. I think that will make things clear to me.

Thanks a lot!!
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Old 11-28-2013, 03:08 PM
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yaser yaser is offline
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Default Re: Point Xj is linear combination of rest of the other points ?

You are most welcome.
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