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-   -   Point Xj is linear combination of rest of the other points ? (http://book.caltech.edu/bookforum/showthread.php?t=4466)

blunderboy 11-27-2013 06:51 AM

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 ?

yaser 11-27-2013 03:27 PM

Re: Point Xj is linear combination of rest of the other points ?
 
Quote:

Originally Posted by blunderboy (Post 11621)
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.

blunderboy 11-27-2013 09:36 PM

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!!

yaser 11-28-2013 03:08 PM

Re: Point Xj is linear combination of rest of the other points ?
 
You are most welcome.


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