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Let f and g be real-valued continuous functions in the vector space C[a, b]. Show that (f. g) = f(x)g(x) dx defines an inner product on C[a, b].

Let f and g be real-valued continuous functions in the vector space C[a, b]. Show that (f. g) = f(x)g(x) dx defines an inner product on C[a, b].

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 21EQ
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Let f and g be real-valued continuous functions in the vector space C[a, b]. Show that g(x) dx defines an inner product on C[a, b].
Transcribed Image Text:Let f and g be real-valued continuous functions in the vector space C[a, b]. Show that g(x) dx defines an inner product on C[a, b].
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