35.2: Inner Product on Functions
- Page ID
- 70174
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Example
Consider the following functions
\[f(x)=3x-1 \nonumber\]
\[g(x)=5x+3 \nonumber\]
\[\text{with inner product defined by }\langle f,g\rangle=\int_0^1{f(x)g(x)dx}. \nonumber\]
What is the norm of \(f(x)\) in this space?
(Hint: you can use sympy.integrate to compute the integral)
What is the norm of \(g(x)\) in this space?
What is the inner product of \(f(x)\) and \(g(x)\) in this space?