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October 10th, 2009, 01:57 PM  #1 
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  lagrange polynomials and polynomials...
Hi, I have a couple of questions: Why is the dimension of Pn(F) n+1? is it because polynomials of degree n is a linear combination of x^n + ....... + x + C? and if you have a lagrange interpolation polynomial, it's unique because the set of generation polynomials is an linearly independent set of n+1 elements, so is that implying that some interpolating polynomial is the only way a polynomial with a certain set of points will turn out? thanks 
October 10th, 2009, 01:58 PM  #2 
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  Re: lagrange polynomials and polynomials...
and I'm wondering why the basis of polynomials couldn't be 2 elements, x and 1? since you could generate any degree polynomial with combinations of these.. but then I guess the reason is that you can't use x as a coefficient.. but I'm not sure why? thanks 
October 13th, 2009, 12:03 PM  #3  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: lagrange polynomials and polynomials... Quote:
Yes x cannot be a coefficient: a coefficient must be a welldefined element of the field the vector space is over (at this point, the field is probably R). Quote:
Quote:
 
October 15th, 2009, 04:14 PM  #4  
Senior Member Joined: Apr 2009 Posts: 201 Thanks: 0  Re: lagrange polynomials and polynomials... Quote:
thanks for the reply, I realized how lagrange polynomials worked after reading the text book over again.. I was just wondering about using "x" as a coefficient. I guess those aren't concretely defined on R thanks  

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