It's kinda a deja-vu from when you first came here and also knew lots of things but not what I would have thought something with that knowledge would already know
@0celo7 I would not strictly speaking call that "linear algebra"
@0celo7 Yeah, so complexify, take the eigenvector to $\lambda$ and the one to $\lambda^\ast$ - the space spanned by these two is obviously invariant, is it not?
@0celo7 A bit of topology and a lot of analysis/geometry, yes
@0celo7 1. You still have some odd gaps. 2. You haven't asked a topology question (except for the boundary thing) that didn't involve some sort of geometry in quite a time, so I can't really tell.
@0celo7 In your adventures in (deRham) cohomology, you yourself noticed that you had gaps in homological algebra and (singular) cohomology. Knowing you, that's neither your fault nor something bad, but I would still show the same confusion as I did back then if I just know got you know you ;)
@0celo7 can you prove the inverse function theorem directly? https://www.physicsforums.com/attachments/inverse-1-jpg.43003/ https://www.physicsforums.com/attachments/inverse-2-jpg.43004/ https://www.physicsforums.com/attachments/inverse-3-jpg.43005/
Sure you'll need to use some sort of definition of union and closure, but at this level most things reduce to rather elementary but potentially tedious exercises in set theory
@0celo7 wow... ignore me, pretty ridiculous to read advanced books skipping the easy theorems they don't even prove, but do insane exercises from the same book
@vzn my question on susskind's paper will be. If EPR=ER, then why we cannot create a large wormhole by bundling many entangled pairs of photons together in a small region?
I discovered that a while ago I made a typo when writing the Rindler metric and I've been copying and pasting the error ever since. So I've had to go back and check every post where I mentioned the Rindler metric to see if it needed correcting. That's why you saw that post suddenly appear on the home page.
@NoahP What do you mean by "correct"? Neither "added together" nor "reinforce" are the technical terms, but if you want to use them to describe constructive interference, then I don't see a problem with either.
@NoahP Saying "I need a more complicated word for the pragmatic purpose of getting a better mark" is highly different from your earlier "This simple word seems ridiculous to me".
@0celo7 https://www.math.ucdavis.edu/~linear/linear.pdf This might help, it goes all the way from the very begining of what is a matrix all the way to the most advanced stuff
Feel free to skip parts you already knew. Most of the stuff here there are nice illustrative examples. Major theorems have proofs that can be followed
some of the proofs use quite a lot of indice, which I assume you are quite comfortable with because of your GR background
Some time later, I might ask MSE what's the best way to optimise a discrete surface. Since the surface has a discrete degrees of freedom, then obviously one cannot define a notion of steepest decent in it via derivatives, or using newton method
The reason such thought came up is because today we discussed about a computation chemistry problem and we compare how the energetics of the compound will change with the number of carbons in the compound.
So the number of carbons is an integer, but the potential energy function of the compound in terms of the reaction prgress is a continous function, so the overall parameter space you have slabs of potential energy surfaces as a function of carbon no. and reacton progress
When I first signed up on a Stack Exchange site and got a profile image, it was this one (see my current user card I'm actually not sure what I look like any more):
Later, I got Area 51 and SEDE profiles, and my user image there was a different identicon. Because reasons I already know. I wou...
@0celo7 it is, every uniformly continuous function is Lipschitz, and $\sqrt{\cdot}$ on a compact interval is uniformly continuous since it is continuous
@yuggib He's looking at $(0,1]$, that's not compact, and uniform continuity does not imply global Lipschitz continuity, $\sqrt{x}$ is a classical counterexample.
It's Lipschitz continuity that implies uniform continuity, not the other way round
$f$ is globally Lipschitz on a (metric) space $X$ if there exists a constant $M$ such that $\forall x,y\in X$ $d(f(x),f(y))\leq M d(x,y)$, and it is locally lipschitz if for any point in $X$ there is a neighbourhood $U$ such that $f\lvert_U$ is Lipschitz
What he said is perfectly fine though. It's equivalent to the locally Lipschitz condition.
@0celo7 Though, you really need "for $x, y$ inside some ball of diameter $\delta$ in $(0, 1]$ there exists an $M$ such that" instead of what you wrote, no?
I mean, you're saying there is an $M$ uniformly for all $x, y$ s.t. $|x - y| < \delta$.
I'm figuring out what to bring with me when I move in to campus. So far I have: shampoo, toothbrush/paste, mouthwash, cleaning supplies, clothes, bedsheets/cover, mattress cover. but I feel like I'm still missing stuff.
I am given this definition:
A function $f:A\subset\mathbb R^n\to\mathbb R^m$ is locally Lipschitz if for each $x_0\in A$, there exist constants $M>0$ and $\delta_0 >0$ such that $||x-x_0||<\delta_0\implies||f(x)-f(x_0)||\leq M||x-x_0||$.
Source: Marsden's Elementary Classical Analysis; note tha...
However, I can't say much about the part I can see. If in the proof (or a remark) Marsden says that that condition means $f$ is locally Lipschitz, that would be plain wrong. — Daniel Fischer ♦Oct 8 '13 at 14:54
DanielF seems to say that's not locally Lipschitz.
@Secret looking fwd to your session, thx for bringing EMdrive to attn of group/ room. personally think it is revolutionary stuff (as far as tying in with emerging "specetime fabric" theory) but everyone else around here is like ho, hum (sigh) :( o_O
In fact, its 2:24 here and I have a big but annoying day tmr, however I am like a zombie and just glued to this computer screen, talk about complete lost of motivation
Example annoying pieces of homework question generator shit I am dealing with
I am telling myself I can handle no longer, once the phD is accpeted, I ma KICK him out
When I first signed up on a Stack Exchange site and got a profile image, it was this one (see my current user card I'm actually not sure what I look like any more):
Later, I got Area 51 and SEDE profiles, and my user image there was a different identicon. Because reasons I already know. I wou...
I am given this definition:
A function $f:A\subset\mathbb R^n\to\mathbb R^m$ is locally Lipschitz if for each $x_0\in A$, there exist constants $M>0$ and $\delta_0 >0$ such that $||x-x_0||<\delta_0\implies||f(x)-f(x_0)||\leq M||x-x_0||$.
Source: Marsden's Elementary Classical Analysis; note tha...
