Recent content by Luna=Luna

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

"It is left as a problem for the reader to show that if [S,T] commutes with S and T, then [e^{tT}, S] = -t[S,T]e^{tT} I'm not sure if I'm missing something here, but i don't even see how it is possible to arrive at this answer. I get: [e^{tT}, S] = e^{tT}S - Se^{tT} Then using the fact...

This is probably going to be a very simple question, i just need justification for a seemingly simple step in a proof. The statement is as follows: An endomorphism T of an inner product space is {0} if and only if \langle b|T|a\rangle = 0 for all |a\rangle and |b\rangle. Now it is obvious if...

I'm sure once again there is some underlying misconception i have of the topic so far, so I will lay out my reasoning and hopefully we can spot where I'm going wrong. The definition I've seen of a metric space is: an ordered pair (M,d) where M is a set and d is a metric, that is a function d...

Hmm, so I've had a bit of a think about where i was going wrong and the comments posted here have helped me get on the right track I believe. Can i just clarify what you mean by "every normed vector space is a metric space" Do you mean every normed vector space is intrinsically a metric...

Ah so the metric space are the most general, i thought it was the least general and that misunderstanding had me going around in circles! Many thanks.

Correct me if I'm wrong here but it is my understanding that vector spaces are given structure such as inner products, because it allows us to use these structured vector spaces to describe and analyse physical things with them. So physical properties such as 'distance' cannot be analysed in...

All this makes sense now. I did have the 'intuition' of splitting the vectors up into orthogonal components, however i decided to do it using a standard basis. This worked in \Re^2 and I could prove the equality by expanding and factorising, but couldn't do it in the general case. The idea of...

I guess these 'tricks' become obvious once you have a firm grasp of the material, and it is this reason I just can't shake that by not learning proofs I'm somehow not really grasping the material. Thanks for that great article from Tao As a physics student it is safe to say my mathematical...

I'm trying to really solidify my maths knowledge so that I'm completely comfortable understanding why and how certain branches of mathematics are introduced in physics and inevitably that leads me to a study of proofs. I usually skip proofs as I found them annoying, unintuitive and just...

sorry it wasn't clear from my post, I've rewritten the post to be a bit more clear. The relationship is: m\trianglerightn, if m-n is divisble by k, where k is a fixed integer.

On the set of Z of integers define a relation by writing m \triangleright n for m, n \in Z. m\trianglerightn if m-n is divisble by k, where k is a fixed integer. Show that the quotient set under this equivalence relation is: Z/\triangleright = {[0], [1], ... [k-1]} I'm a bit new the subject...

Thank you for the replies. Makes sense now. Thanks for taking the time to go through all the working as well vanhees, was helpful in checking my own working through it.

https://dl.dropboxusercontent.com/u/22024273/vectorpotential.png In the above passage, can someone explain to me where (3.102) comes from?

Thanks for the responses! I knew it had to be missing something basic! Makes sense now.