Inner Product of Polynomials: f(x) & g(x)

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Homework Help Overview

The discussion revolves around defining the inner product of two polynomials, specifically focusing on the polynomial f(x) = 3 - x + 4x² and its inner products with other polynomials f1, f2, and f3. Participants are exploring the implications of the inner product definition and the role of the polynomial g(x).

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the purpose of the polynomial g(x) in the context of the inner product. There is discussion about substituting specific polynomials into the inner product formula to compute the values.

Discussion Status

Some participants have provided guidance on substituting the polynomials into the inner product formula. There is an ongoing exploration of how to approach the calculations for the inner products.

Contextual Notes

Participants are working under the constraints of the problem statement, which defines the inner product and specifies the polynomials involved. There is a focus on understanding the setup and implications of the inner product without resolving the calculations.

grewas8
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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
 
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g is an arbitrary polynomial, so, g could be f1, g could be f2, etc.
 
so do i just sub. f1 to find <f|f1> and take integral of f(x) and f1(x) ?
 
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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