I'm a grad student in math and I can tell you. I dislike the whole (integral (f^p))^1/p Where does this logic come from. Like, let me do this....... (f^p)^1/p then it would all cancel out and be pointless. Like who thought of this clunky notation and set-up? Like, it feels not elegant.
But it doesn't cancel. You can't move the 1/p underneath the integral sign automatically. For example take p = 2, f(x) = x on the interval (0,1). Then ||f||_2 = integral_0 ^1(x^2 dx) ^ (1/2) = (1/3)^1/2 = 1/sqrt(3). Whereas if you could move the 1/p into the integral, the answer would be 1/2. It's meant to be an analogue of the euclidian norm on R^n, where you take the square root, but here you can take 1/p. Also iirc this makes it easier to define the dual space. Apologies for the bad notation, but youtube comments aren't great for math notation.
@@sethaaronson4011 I know it doesn't cancel, but this idea is so "messy" that it doesn't appeal to me. And its so close to canceling the 1/p raised to the p that you question, what is the point. I'm a math major, I like nice and elegant ideas and this comes across as really convoluted in terms of the motivation. We want to see if the integral will blow up and so we use the Lp norm. Like, there has to be a better way of doing this to get the same result.
@@sethaaronson4011 In general I don't like the concept of norms and we talked about the dual space in my analysis class, but I don't get it. There were tons of concepts in grad school that we talked about, but I didn't understand half of it. The only time I actually learned what a vector space was, was when I taught Linear Algebra for myself and figured it out. I don't think I had the best of teachers.
20:13 the summary was fantastic.
Thank you for the really clean and clear lectures. It seems that a large amount of effort was put into them.
I'm a grad student in math and I can tell you. I dislike the whole (integral (f^p))^1/p
Where does this logic come from. Like, let me do this....... (f^p)^1/p then it would all cancel out and be pointless. Like who thought of this clunky notation and set-up?
Like, it feels not elegant.
ok
But it doesn't cancel. You can't move the 1/p underneath the integral sign automatically. For example take p = 2, f(x) = x on the interval (0,1). Then ||f||_2 = integral_0 ^1(x^2 dx) ^ (1/2) = (1/3)^1/2 = 1/sqrt(3). Whereas if you could move the 1/p into the integral, the answer would be 1/2. It's meant to be an analogue of the euclidian norm on R^n, where you take the square root, but here you can take 1/p. Also iirc this makes it easier to define the dual space. Apologies for the bad notation, but youtube comments aren't great for math notation.
@@sethaaronson4011 I know it doesn't cancel, but this idea is so "messy" that it doesn't appeal to me. And its so close to canceling the 1/p raised to the p that you question, what is the point.
I'm a math major, I like nice and elegant ideas and this comes across as really convoluted in terms of the motivation.
We want to see if the integral will blow up and so we use the Lp norm. Like, there has to be a better way of doing this to get the same result.
@@sethaaronson4011 In general I don't like the concept of norms and we talked about the dual space in my analysis class, but I don't get it.
There were tons of concepts in grad school that we talked about, but I didn't understand half of it. The only time I actually learned what a vector space was, was when I taught Linear Algebra for myself and figured it out. I don't think I had the best of teachers.
Automated motion-tracking is a solution searching a problem. :/
This automated camera has not mastered neural networks yet