Showing That a Function Is an Inner Product In
Chapter 5, Problem 34(choose chapter or problem)
Showing That a Function Is an Inner Product In Exercises33 and34, show that the function defines an inner product for polynomials \(p(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n}\) and \(q(x)=b_{0}+b_{1} x+\cdots+b_{n} x^{n}\).
\(\langle p, q\rangle=a_{0} b_{0}+a_{1} b_{1}+\cdots+a_{n} b_{n}\) in \(P_{n}\)
Text Transcription:
p(x) = a_0 + a_1 x + cdots + a_n x^n
q(x) = b_0 + b_1 x + cdots + b_n x^n
langle p, q rangle = a_0 b_0 + a_1 b_1 + cdots + a_n b_n
P_n
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