Parseval's Identity:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3. LADW #5.2.3: Let {v₁,..., Vn} be an orthonormal basis in V.
(a) Prove that for any x = Σαν and y = Σβιve, we have that
k=1
n
(b) Deduce from this the Parseval's Identity:
72
n
k=1
(x, y) = Σακβκ.
k=1
n
(x, y) = Σ(x, vk) (y, vk).
k=1
Note: Part (a) shows us the usefulness of an orthonormal basis B. It says that we
can compute the inner product of two vectors in V by computing the standard inner
product in F (instead of in V) of the coordinate vectors with respect to B.
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