(a) Suppose y is the set of all even functions in C[-1, 1]. Find the orthogonal complement y¹ of y in C[-1, 1] under the inner product on C[-1.1] given by (x,y)= £₁x(1) y(1) d (C[-1. 1] - the space of all continuous real valued functions on [-1, 1]).
(a) Suppose y is the set of all even functions in C[-1, 1]. Find the orthogonal complement y¹ of y in C[-1, 1] under the inner product on C[-1.1] given by (x,y)= £₁x(1) y(1) d (C[-1. 1] - the space of all continuous real valued functions on [-1, 1]).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(a) Suppose y is the set of all even functions in
C[-1, 1]. Find the orthogonal complement y1
of y in C[-1, 1] under the inner product on
C[-1. 1] given by (x, y) = [',x(1)y(1)dt.
(C[-1. 1] - the space of all continuous real
valued functions on [-1, 1]).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15b7304-cc73-4505-92c3-23aa2fda4f71%2F3c50a5cf-0ebe-45ed-8b72-4cc0ed1b9cd2%2Fiswgwj6i_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Suppose y is the set of all even functions in
C[-1, 1]. Find the orthogonal complement y1
of y in C[-1, 1] under the inner product on
C[-1. 1] given by (x, y) = [',x(1)y(1)dt.
(C[-1. 1] - the space of all continuous real
valued functions on [-1, 1]).
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