Matrix exponential question

Sadly, you guys are slowly turning this subforum into a joke.

 

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I'm quite happy about it, actually.

Have you found out what a C*-algebra is yet?
How about Borel spaces?

Have you ever heard of geometric quantization?
Algebra of a topology?

P.S. Stick this lot up your left one:

You could have used this thread as an opportunity to learn something, but instead it's become a medium for you to demonstrate your habit of nailing one of your feet into the floor.
So have you been doing any homework? Do you now know how to explain why B is either one of:

* A basis. What vector space does it form a basis of, and why is it a basis?
* A Borel measure. What is the underlying topological space? What are the corresponding open sets that generate the Borel \(\sigma\)-algebra?

I actually do know why, but you, being a total math-dweeb, seem to have zero idea.
Therefore your advice probably isn't worth my consideration.
So I will be ignoring you altogether, isn't that nice for you? No more annoying ideas for you to get all upset about...

 

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Firstly, I've done much more work on Hilbert spaces than you, which considering you refer to me as 'young man', must be all the more depressing for you. The fact I was able to do the question you initiated this thread with and then explain a multitude of concepts relating to your question which you didn't understand seems to have passed you by.

Do you know what a Hilbert space is? It's a vector space with an inner product which is complete. 0 and 1 define a vector space but you don't know if it's complete, nor is any mention of an inner product made. \(|0\rangle\) and \(|1\rangle\) define a vector space too. And since the \(|\rangle\) notation is predefined when working within quantum mechanics to refer to a vector space over C, with an inner product defined on it via \(\langle | = (|\rangle)^{\dag}\) and \(\langle|\rangle \in \mathbb{C}\), then we have a Hilbert space.

Why are you trying to down talk to myself andf guest when it comes to quantum mechanics and mathematical areas like vector spaces, Lie groups/algebras and Hilbert spaces. Time and again on these forums we've demonstrated we know about them. Far in excess of what you know and can do involving them.

You keep saying to us "Find out what a Borel measure is!!!" when you refuse to find out what a basis is. Or how to do vector calculus. Or linear algebra. Something I'm paid to teach 1st years, you can't do. And yet you whine about how we should be looking up 3rd or 4th year material to keep up with you.

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You really are crackers, aren't you?

 

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Why in the world is this silly thread still alive?

 

I can see that wee spell in America did your manners no good alphanumeric.

Oh well, some you win.

 

Vkothii was more than happy for myself, Guest, Rpenner and perhaps a few others to reply when helping him with a specific question. When our help expanded to say "The best way to learn subject X is to first learn subject Y, we know, we've learnt them and that's how everyone everywhere teaches them" he suddenly started saying "Typical". So if he knows/thinks that it's typical for us to insult people, why was he so happy to accept the honest, helpful and lengthy help from us in the first few pages?

He, like you, was fine until someone corrected him on something. Why oh why do so many people have a problem with being told "You're wrong." by someone who is 'in the know'. Right now I'm having email discussions with people who are vastly more knowledgable than myself in the area of Lie algebras. At the end of each of my emails I'll say something like "I'm sure at some point I've said something which is completely wrong and pretty basic at that, but that's the purpose of me originally contacting you. I can't move on with what I want to do until I've nailed down the fundamentals".

Vkothii has completely skipped 3 years of linear algebra fundamentals and tried to jump into graduate work. And surprise surprise, he's failed miserably at it. Wow. Haven't seen that before! No, wait.... you do it all the time too. Still trying to claim you're studying the Riemann curvature tensor when you don't know the difference between a metric and a vector and you haven't even got to university level physics yet? Vkothii is just trying to make the same claims as you do, except he's doing it in linear algebra while you do it in quantum mechanics and relativity.

Just because you're kindred spirits doesn't stop you both being idiots.

 

No, I suddenly started saying something else altogether - along the lines of: "shit, it's really hard to get you guys to see past your paradigm". Also: "for fucksake, I know what an approximation is".
What I was thinkibg, however, was somewhat different, (and a little more devious).
But since deviation seems to be the game you all want to play - into such imponderables as whether I know how to add or subtract, I thought I'd add my own contribution to the local gradient - OK?

All that's failed here is a connection - the channel appears to be overwhelmed with noise, from various egos.

Since none of you math experts have ever done any real physics, or knows anything about how a transistor works, or even what something as straightforward as a bloody circuit is, you resort to accusations and make all kinds of totally irrational connections that don't actually exist. It looks so intelligent??

Why do you have such a problem with being told "math doesn't explain everything". Or even: "reality behaves mathematically, but reality isn't made out of mathematics".

Some of you seem to think it is??

Just because you're interested in science doesn't stop you being a narrow-minded plonker.

 

You guys are bloody hopeless. I really should give up on you and your "math-expertism", because obviously all it's done for you is let you make entirely subjective decisions, select the conclusion that fits your swell-headed paradigm, of your personal ability to discern something.

That sentence I typed into this thread a while back kind of sums up what trying to ask anything, even remotely mathematical (i.e. that includes a bit of math symbology) end up like.
It's such a waste of time.

Therefore, I give up. I will not post any math that poses any question whatsoever, in your direction.
My expectation being that doing such a thing has only one inevitable outcome. Which is: "A WASTE OF MY TIME". (see how that's in caps?)

 

Except you didn't understand the approximation that your question asked for. The O(n) notation used in algorithm measurements was a different approximation, because it involved large n, while the question you were asked is only valid for small t. Infact, if you understand the difference between a Lie group and a Lie algebra you'll know that a Lie algebra is defined within the neighbourhood of the identity of the group and you cannot move an arbitrary distance away from the identity and expect the relationship between the Lie group and the exponentiation of the Lie algebra to always be the same. This is because there are different Lie groups which have the same Lie algebras, up to an isomorphism, and the difference in the Lie groups comes when you are no longer in the region where your exponentiation of the Lie algebra is a simple matter.

So, as we said many times, you didn't know what that approximation was.

Actually we continued to try to get you to understand the difference between "Up to O(x^n)" and "Is of O(x^n)" for both large and small x and n. You then went onto talking about Borel measures and other things which didn't relate to the quantum mechanics you were doing. I've seen things where a perturbation is done via a magnetic field and elements of a group like \(e^{i\sigma.B}\) or whatever and wether or not that's a measure is irrelevent to how you would do the question. You use commutation relations on the sigmas, using the identity you'd previously worked out, and you find how the energy levels of your system have changed. If you're desperate, I'm sure I can find a few homework questions from my old course covering that to illustrate my point.

You whined about algorithms, while Guest, Rpenner, myself and others gave specific explainations and examples as to why your "But I did O(n) stuff in algorithms!" wasn't applicable. That's derivation. From you.

Oh, more deviation. So because we haven't done something irrelevent to the original question, we're not fit to tell you how to do the original question? Well my mum, a doctor, can't change a gear box in a car, does that mean she can't tell a mechanic he's got cancer?

You asked a question, several people demonstrated they knew how to do it, in a variety of ways and the general theory around the question. You were corrected. You didn't like it. Now you are engaged in deviation by saying we're being snobby for correcting you because you're able to apply your knowledge and we've never seen some of the stuff you have.

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Give me a break.

Oh and things like X-ray crystallography, p-n transistors, electron energy bands in materials and lattice vibrations are all covered in such courses like "Applications of Quantum Mechanics" at Cambridge. If you want to do other applied things which involve quantum mechanics, you can do phonons in superfluids or electrodynamics within BECs. I know people doing such things, having done PhDs in 'quantum light and matter', which are quite practical or just the mathematical modelling of them.

Where did we suddenly go "OMG no, you're wrong!!" when you said "Maths doesn't explain everything". Infact, where did you even say that?

The length of this thread has occured because you refuse to accept correction in an area you're unfamiliar with from people who know more than you about this area. You also refuse to accept advice. You don't go to a problems class to ask questions, only to deliberately ignore the answer, so why do you come to this forum to ask for help only to ignore it?

Are you like Reiku, you want to be seen to be doing very complicated stuff, so you try to waffle about it and then when corrected you throw a tantrum? Given you completely skipped all the precursor courses and you think a computer science degree lets you jump blindly into a maths postgrad qualification, you are at the very least naive. And your errors in this thread seem to have done nothing to change that. Why not? If you find yourself struggling with a problem and you know you don't understand the basics, why not go back and learn the basics?

I got a book out of my uni library entitled "Mirror Symmetry and Algebraic Geometry" a while ago. I know a bit about both of those topics. By page 3 I was completely lost. Rather than continue to read on, wasting my time, I took it back and got out a book which explained algebraic geometry to me. Thus helping me build up knowledge from my current limits. No point in wasting my own time. Yet you want to waste yours. Wow, that's clever.

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Well, of course since I didn't even go to school, I don't even know what a number is, never mind how to add one of them to another number.

It's so goddam easy, to get you morons to believe you're dealing with an uneducated idiot.
I consider that being here asking questions of people like you, is probably kind of an idiotic thing to do, sure. I mean obviously, you're on some other kind of planet. Planet Janet, perhaps?

I do know what a Taylor expansion is, I do know what an order approximation is.
You only know what a polynomial is, probably your definition is a page or so long.

Guess what else? Unlike you and everyone else here who is so bloody sure about their opinion, I also understand why Prof Lloyd makes a point of having students derive it and the Pauli matrices. An insight into information processing with fermions, etc.
But you don't.

 

You're doing an awfully good job.

 

So are you, Guest old man. Absolutely.

Have you managed to pull that nail out?

 

I'm not sure how to answer. Are you still in character?

 

Which one would you prefer?

 

I'm not sure I can tell the difference. Anyway, this is silly. Please, carry on with your monologues. You mentioned fibre bundles, geometric quantization, C*-algebras - I'd be really interested in seeing you post more about these things.

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Oh bullshit.

 

Vkothii, aren't you a bit concerned that it's so difficult to tell the difference between you pretending to be an idiot and you?

 

Alphanumeric,

aren't you a bit concerned that its so difficult to tell the difference between you pretending to be a moron and you?

 

I think we've seen enough here.

I've been a bit negligent in regards to this thread, and I want to apologize for that.

That being said, off to the Cesspool!

 

Firstly, people in glass houses shouldn't throw stones, since you're another one who bites off more than he can chew and refuses to accept correction. Secondly, I'm able to back up my claims about what I can and can't do or what I do or don't know. You can't.

So pipe down unless you want to show off more of your hypocrisy and ignorance. Which, experience tells me, you probably do.