Let C[a, b] denotc the set of continuous functions f : [a, b] → R. Given any two functions S,9 € C[a, b], let (S, 9) = | S()g(t)dt. S(1)g(t)dt. Prove that the above bilincar form is bilincar, symmetric and positive (that is, (f, f) > 0 for all f € C[a, b]). You do not have to prove that this bilincar form is definite (that is, if (S, S) = 0, then f = 0).
Let C[a, b] denotc the set of continuous functions f : [a, b] → R. Given any two functions S,9 € C[a, b], let (S, 9) = | S()g(t)dt. S(1)g(t)dt. Prove that the above bilincar form is bilincar, symmetric and positive (that is, (f, f) > 0 for all f € C[a, b]). You do not have to prove that this bilincar form is definite (that is, if (S, S) = 0, then f = 0).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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