Consider the function, prove that it's bilinear, symmetric, and positive definite
[Orthogonal Polynomials]. Consider the following bi-valued function defined on the space of polynomials of degree ≤ 2:
(Image 1)
For whichever polynomials p(x), q(x) ∈ P≤2. Consider the following polynomials:
p0(x) = 1, p1(x) = x, p2(x) = (3/2 )x² − 1/2 .
(a) Prove that F is bilinear, symmetric, and positive definite
(b) Prove that the family (p0, p1, p2) is an orthogonal basis of P≤2.
28
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

1.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 842 views
- $8.00
Related Questions
- Algebraic and Graphical Modelling Question
- Eigenvalues and eigenvectors of $\begin{bmatrix} 3 & 2 & 4 \\ 2 & 0 & 2 \\ 4 & 2 & 3 \end{bmatrix} $
- Character of 2-dimensional irreducible representation of $S_4$
- Linear Algebra Assistance: Linear Combinations of Vectors
- Let $H$ be the subset of all 3x3 matrices that satisfy $A^T$ = $-A$. Carefully prove that $H$ is a subspace of $M_{3x3} $ . Then find a basis for $H$.
- Stuck on this and need the answer for this problem at 6. Thanks
- Frontal solver by Bruce Irons? Am I using the right Algorithm here?
- Length of a matrix module