Recent content by yiorgos

Modification: I mistakenly added also "identity matrix" to previous post. Please ignore this from the list of matrices I have tried.

Let a positive definite matrix A be factorized to P and Q, A=P*Q and let an arbitrary matrix B. I am calculating the relative error of the factorization through the norm: \epsilon = \left\| \textbf{A}-\textbf{PQ} \right\| / \left\| \textbf{A} \right\| which gives \epsilon <1\text{e}-16 so I...

So in short you are saying that this transformation doesn't hold?

Thanks for the answer. You are right about the particular transformation yet that was just a naive example I gave. I am sure there exist "clever" ways to achieve this. For example http://en.wikipedia.org/wiki/Logarithm_of_a_matrix I don't know if that helps more but what I actually...

I am looking for a transformation that relates a matrix product with a matrix addition, e.g. AB = PA + QB Is there any such transformation? Thnx

How is this generalized to nxn matrices?

I forgot to mention that I know for \phi(x) that it is defined only in [a,b] and I'm interesting particularly for a domain of the form [-a,a]. Additionally, I expect \phi(x) to be continuous and symmetric about zero. Would these properties help by any means?

Thank you for the reply. So, you say that if |K|<1 then \varphi vanishes? One more question. Since my kernel is not of a specific form, is it more convenient to take h(t)=g(x)*\varphi(t) and translate the initial equation to the form \varphi(x)= \int_a^b K(x,t)h(t)dt which is a Fredholm...

Hi, during the analysis of a problem in my phd thesis I have resulted in the following equation. \varphi(x)= \int_a^b K(x,t)\varphi(t)dt which is clearly a homogeneous Fredholm equation of the second kind The problem is that I can't find in any text any way of solving it. Solutions are...

Thank you badphysicist. I'm working on your advice. I'll come back with feedback when I find some sort of solution

anyone please?

I would like to ask for your help to solve a problem concerning the well-known case of an electron inside a well of defined potential. I've already studied the case of the 1dimensional infinite potential well, but my case is a bit more complicate since it includes a 2D space and different...

Physics is not a matter of applications, this is an Engineering subject. Moreover, If the string theories and the M-theory are correct then the Maxwell equations ought to have a multi-dimensional form.

My main question is if the Maxwell equations have been generalized to include extra dimensions in an generally accepted form, or is it still under investigation? I've already read http://arxiv.org/pdf/hep-ph/0609260v4 but I didn't quite like the add-hoc assertion We assert that in all...

That's why the charge density is increased as we get closer to the edge. If you can quantify the above density then you can relatively easy calculate the force between them. But as I said I can't find any formula of calculating that.