LFD Book Forum Point Xj is linear combination of rest of the other points ?
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#1
11-27-2013, 05:51 AM
 blunderboy Junior Member Join Date: Aug 2013 Posts: 5
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 ?
#2
11-27-2013, 02:27 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Point Xj is linear combination of rest of the other points ?

Quote:
 Originally Posted by blunderboy 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 , the vectors are two-dimensional () because of the zeroth coordinate, but to answer your specific question, has many solutions, for instance, and .
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#3
11-27-2013, 08:36 PM
 blunderboy Junior Member Join Date: Aug 2013 Posts: 5
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!!
#4
11-28-2013, 02:08 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Point Xj is linear combination of rest of the other points ?

You are most welcome.
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