- #1
pr0me7heu2
- 14
- 2
Suppose f(x)= -2x+1 is a vector in the vector space C[0,1].
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?
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?