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Let V be the real inner product space consisting of the space of real-valued continuous functions on the interval, -1= :| f(t)g(t)dt. Let W be the subspace of odd functions, i.e., functions satisfying f(-t) = – f(t). Find the orthogonal complement of W.

Let V be the real inner product space consisting of the space of real-valued continuous functions on the interval, -1= :| f(t)g(t)dt. Let W be the subspace of odd functions, i.e., functions satisfying f(-t) = – f(t). Find the orthogonal complement of W.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Let V be the real inner product space consisting of the space of real-valued continuous functions on the interval, -1 <t< 1, with the inner product < f,g >= :| f(t)g(t)dt. Let W be the subspace of odd functions, i.e., functions satisfying f(-t) = – f(t). Find the orthogonal complement of W.
Transcribed Image Text:1. Let V be the real inner product space consisting of the space of real-valued continuous functions on the interval, -1 <t< 1, with the inner product < f,g >= :| f(t)g(t)dt. Let W be the subspace of odd functions, i.e., functions satisfying f(-t) = – f(t). Find the orthogonal complement of W.
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