How do you compare function norms if the functions are defined over different regions?
Any benefits of using L2 norm rather than L1?
What is the relation between the norm of a function and the area covered by the function and the x-axis?
Why does the function need to be in the interval [0,1]?
If we have a scalar multiplication with ratio a for f, as a result of sqrt(a^2) don't we technically get both 'a' and '-a'? Do we just ignore the '-a' part of the solution because a norm must be non-negative?
Is there a reason that the L2 norm is written as L^2 but pronounced as "L2" (rather than "L squared")?
When we say "well-defined integral", do we disallow functions with integrals that evaluate to infinity?
Do we use other types of norm in graphics, like the L1 norm or the L-infinity norm, or we just go with the L2 norm because it makes most sense geometrically with the Pythagorean theorem. Is there a specific reason to choose each of them?
In this case, we are looking at functions defined over [0,1]. If we have functions defined over a larger range, would the definition of the L2 norm be modified to integrate over that larger range instead?
This surely meets the criteria of norms. However, why we are having the range limitation here? I feel according to the definition, we can have whatever ranges we like.
It seems like it satisfies all the properties, except that there are multiple potential "zero vectors", since you could have a function where it is 0 for all x, or a function like sin which for one period will have an integral of 0. This seems to be O.K. though?
Can we transform functions whose squares don't have well defined integrals over [0, 1] but has well defined integrals over another interval [a, b] to [0, 1] and then calculate the L2 norm for them? Would there be anything interesting about the result?
Can we use a general interval [a,b] instead of [0,1]? or is [0,1] just a convention?
What modifications to the norm would need to be made to compute a valid norm over a general interval?
How can we determine which kind of norm is more suitable for a specific situation?
In graphics, do we ever use other "n norms", like the 1 norm or 3 norm or even infinity norm?
I might've missed this, but where did "L2" come from? Is this only specific to functions or is it referencing something else?
Do we 'normalize' functions by dividing by their L2 Norm similar to how we normalize vectors?
Is the L2 norm purely defined over the [0,1] range or could that range be arbitrarily chosen? Also, what does this metric really measure? What is the function of the L2 norm?
Why do we sometime use L1 norm instead of L2 norm?
Are there notions of an L2 norm but for functions that have a greater domain than [0,1]. What about non-continuous functions?