For those in quant finance, how much of this is useful in your day to day?
There is no need for it. Here is a simple replacement: https://keithalewis.github.io/math/um1.html.
Readit Newskeithalewis commented on Introduction to Stochastic Calculus jiha-kim.github.io/posts/... · Posted by u/ibobev
"I don't understand this complexity so this means it shouldn't exist"
Linus wrote it, so there's got to be a pony in there somewhere. He's the first person in the world to figure out version control software. /s
Thank you for your diligence in explaining complicated topics in a way that makes them accessible to people trying to learn what people before them figured out. You are a true educator that seems have found a place to support you to continue doing that.
Are you concerned that your git exposition is much longer than the other guides you have produced?
I don't exactly know what you mean but from your hint I found the uh, clarifying bedtime story:
https://arxiv.org/abs/2302.09687
(On functions of 3rd-order "tensors")
((Whereas matrix-functions are of 2nd-order "tensors"))
Playground: https://gitlab.com/katlund/t-frechet
(MATLAB)
The Wikipedia page on this is sufficient. If F:X -> Y is a function between normed linear spaces then DF:X -> L(X,Y), where L(X,Y) is the vector space of linear operators from X to Y, satisfies F(x + h) = F(x) + DF(x)h + o(h). A function is differentiable if it can be locally approximated by a linear operator.
Some confusion arises from the difference between f:R -> R and f':R -> R. It's Fréchet derivative is Df:R -> L(R,R) where Df(x)h = f'(x)h. Row vectors and column vectors a just a clumsy way of thinking about this.
BTW, all you need in order to publish on arixv.org is to know a FoF. There is no rigorous peer review. https://arxiv.org/abs/1912.01091, https://arxiv.org/abs/2009.10852.
This is standard notation that's been used for decades.
"This book aims to standardize the notation for tensor diagrams..."
https://youtu.be/zELbzXAmcUA?t=73
The author also seems to be unaware of Fréchet derivatives.
This is incomplete, incorrect, and irrelevant. Standard notation already exists. I'm sure it is fun to draw squiggly lines and some people enjoy reinventing the wheel. Spend some time learning what others have taught us before striking out on your own lonely path.
keithalewis commented on Kalman Filter Tutorial kalmanfilter.net/default.... · Posted by u/ColinWright
> Just stop whining about it in public.
I'm curious if this is how my reply came across?
Your statement "the best path forward for me understanding is a path that can maintain that curiosity" comes off as entitled. Only you owe yourself that.
"I can play with Arnold's cat and, slowly, through no scientific rigor..." You are fooling yourself into believing you understand if you leave out rigor. If your post has the words "I" and "me" in every other sentence, maybe you should consider whether or not you are adding value for others in the online discussion.
I doesn't cost you anything to ask other people to do things for you, and you will no doubt find other thoughtless people chiming in about your right to do that. If everything you need is not at your fingertips already, maybe no amount of handholding will help.
Dead Comment
Second, humans are conscious of the things we are doing. We can write articles about it and make choices about how we will change the environment in the future. We cannot discuss things with wolves in Yellowstone about how they are changing the area. The cinnamon trees in Hawaii can’t get together and decide how to share space with other plants.
And finally, always have at least three items when listing things.