Suppose f(x)= -2x+1 is a vector in the vector space C[0,1].(adsbygoogle = window.adsbygoogle || []).push({});

Calculating the norm (f,f) results in 1/3.

I'm a little confused.

So on [0,1] the function is a straight line from (0,1) to (0,-1).

So I thought I could simply takes this line segment and turn it into a directed line segment originating from the origin. So it would be equivalent to the vector v= 0i - 2j (right?)

, so then ||v|| = sqr(0^2 + (-2)^2) = 2

So the length of vector v is 2.

Why is this different from the norm (f,f)? Shouldn't they be the same?

...or am I completely missing the point here of the norm / inner product of the function?

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# Norm of a Function vs. Length of a Vector

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