Gram-Schmidt help!!
Let Ω = [−1, 1] ⊂ R and consider Π2(Ω)
Given that B = {p1, p2, p3} is a basis of Π2(Ω) and that <f | g> = f(−1)g(−1) + f(0)g(0) + f(1)g(1)
does defines an inner product on Π2(Ω), consider the following:
Use the Gram-Schmidt process to create an orthonormal basis G = {q1, q2, q3} of Π2(Ω) with the
property that span{p1, . . . , pk} = span{q1, . . . , qk} ∀k ∈ {1, 2, 3}.
I don't know where to start on this question so any help will be appreciated.
Given that B = {p1, p2, p3} is a basis of Π2(Ω) and that <f | g> = f(−1)g(−1) + f(0)g(0) + f(1)g(1)
does defines an inner product on Π2(Ω), consider the following:
Use the Gram-Schmidt process to create an orthonormal basis G = {q1, q2, q3} of Π2(Ω) with the
property that span{p1, . . . , pk} = span{q1, . . . , qk} ∀k ∈ {1, 2, 3}.
I don't know where to start on this question so any help will be appreciated.
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