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35.2: Inner Product on Functions

Last updated

Sep 17, 2022
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- 35.1: Inner Products
- 35.3: Assignment wrap-up

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from IPython.display import YouTubeVideo
YouTubeVideo("8ZyeHtgMBjk",width=640,height=360, cc_load_policy=True)

from IPython.display import YouTubeVideo
YouTubeVideo("8ZyeHtgMBjk",width=640,height=360, cc_load_policy=True)

Example

Consider the following functions

$f(x)=3x-1 \nonumber$

$g(x)=5x+3 \nonumber$

$\text{with inner product defined by }\langle f,g\rangle=\int_0^1{f(x)g(x)dx}. \nonumber$

Question 5

What is the norm of $f(x)$ in this space?

(Hint: you can use sympy.integrate to compute the integral)

Question 6

What is the norm of $g(x)$ in this space?

Question 7

What is the inner product of $f(x)$ and $g(x)$ in this space?

Example

Question 5

Question 6

Question 7

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