I'm a little confused with the notion of a norm for the second and third pairs of examples. The concept of "big" seems too handwavy for the functions and the images. Is there a more concrete numerical definition for these?
helloCrystal
I am guessing that for the third example we can interpret the norm as the brightness?
And for the second example we can see norm as the area under the curve.
dushuren
Can we calculate the norm of functions like circles? For circles, there is not a definite answer for an input.
Zhuoqian
The norm of functions is defined in terms of integrals. See http://15462.courses.cs.cmu.edu/fall2018/lecture/linearalgebra/slide_029. See also the definition of function inner products.
I'm a little confused with the notion of a norm for the second and third pairs of examples. The concept of "big" seems too handwavy for the functions and the images. Is there a more concrete numerical definition for these?
I am guessing that for the third example we can interpret the norm as the brightness? And for the second example we can see norm as the area under the curve.
Can we calculate the norm of functions like circles? For circles, there is not a definite answer for an input.
The norm of functions is defined in terms of integrals. See http://15462.courses.cs.cmu.edu/fall2018/lecture/linearalgebra/slide_029. See also the definition of function inner products.