Recent content by Luck0

I don't know if this is related to what you really have in mind, but your posts made me remember of Dyson's interpretation of random matrices ensembles, outlined here: https://aip.scitation.org/doi/abs/10.1063/1.1703773 Basically, he considers random matrices enembles as ensembles of some...

Suppose I have a hermitian ##N \times N## matrix ##M##. Let ##U \in SU(N)## be the matrix that diagonalizes ##M##: ##M = U\Lambda U^\dagger##, where ##\Lambda## is the matrix of eigenvalues of ##M##. This transformation can be considered as the adjoint action ##Ad## of ##SU(N)## over its...

I see. Thanks for the answers!

I'm more interested in algebraic properties. In fact, I want a closed form for the coefficients of ##M^{-1}## in powers of ##\epsilon##. The problem is that in my calculation, if I make ##A \to A + \delta I##, I'll have to keep terms in ##\delta##, which is something I want to avoid, because it...

Suppose I have a matrix M = A + εB, where ε << 1. If A is invertible, under some assumptions I can write e Neumann series M-1 = (I - εA-1B)A-1 But if A is not invertible, how can I expand M-1 in powers of ε? Thanks in advance

It turns out that doing my calculations with Λ(U) is way more easy than doing it with U. The only problem is that the difficulty now is identifying the independent components

Let U ∈ SU(N) and {ta} be the set of generators of su(N), a = 1, ..., N2 - 1. The action of the adjoint representation of U on some generator ta can be written as Ad(U)ta = Λ(U)abtb I want to characterize the matrix Λ(U), i. e., I want to see which of its elements are independent. It's known...

Of course! I was mixing things Yes, you're probably right, I will give it a try. Thank you!

Yes, this is what I thought too but I'm having trouble with the following: in the Lie algebra case, we take the generators of Cartan subalgebra and diagonalize them in the adjoint representation. The other generators (let's call them k) of the algebra are given by eigenvectors of ad(h)...

So, we know that if g is a Lie algebra, we can take the cartan subalgebra h ⊂ g and diagonalize the adjoint representation of h, ad(h). This generates the Cartan-Weyl basis for g. Now, let G be the Lie group with Lie algebra g. Is there a way to diagonalize the adjoint representation Ad(T) of...

This is very helpful, thanks!

Some function f: G -> ℝ, where G is the Lie group. For example, the Itzykson-Zuber integral ∫dUexp(-tr(XUYU†)), where X, Y are n x n hermitean matrices and U ∈ U(n)

I'm not sure if this question belongs to here, but here it goes Suppose you have to integrate over a lie group in the fundamental representation. If you pass to the adjoint representation of that group, does the Haar measure have to change? I think that it should not change because it is...

Yes, I discovered that my problem is not with the software, but with the assymetry in the intensities peaks. I'm trying to use split Pearson VII to refine my data now and I'm getting good results.

I'm analyzing data from XRD on a FeSeTe sample, and can't figure out how to match the calculated intensities with the observed ones. I'm having a hard time with this program, can someone help me?