Inner product

  • Thread starter grewas8
  • Start date
  • #1
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Homework Statement


Define the inner product of two polynomials, f(x) and g(x) to be
< f | g > = ∫-11 dx f(x) g(x)
Let f(x) = 3 - x +4 x2.
Determine the inner products, < f | f1 >, < f | f2 > and < f | f3 >, where
f1(x) = 1/2 ,
f2(x) = 3x/2
and
f3(x) = 5(1 - 3 x2)/4
Expressed as a column vector these inner products are given by?


Can anyone help me understand this question, what is the point of g(x)? any help on approach would be helpful
 

Answers and Replies

  • #2
George Jones
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g is an arbitrary polynomial, so, g could be f1, g could be f2, etc.
 
  • #3
16
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so do i just sub. f1 to find <f|f1> and take integral of f(x) and f1(x) ?
 
  • #4
614
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Yes, you just sub in the appropriate polynomials. So the first one will be < f | f1 > = ∫-11 dx f(x) f1(x) = ∫-11 (3 - x +4 x2) (1/2) dx
 

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