Recent content by lukluk

Often people asks how to obtain a positive definite matrix. I would like to make a list of all possible ways to generate positive definite matrices (I consider only square real matrices here). Please help me to complete it. Here M is any matrix, P any positive definite matrix and D any...

great thanks!

Fisher matrix=(minus the) average of the second derivative of the log-likelihood with respect to the parameters It seems to me the Fisher matrix for Gaussian data is invariant with respect to any (non-singular) linear transformation of the data; if correct this is a very useful property...

update: I found that taking the Fourier transform of both sides one can show that g(y)=∫dk (1/f(k)) eikx up to some factor of 2π, where f(k) is the Fourier transform of f(x).

I was wondering which are the properties of functions defined in such a way that ∫dx f(y-x) g(x-z) = δ(y-z) where δ is Dirac delta and therefore g is a kind of inverse function of f (I see this integral as the continuous limit of the product of a matrix by its inverse, in which case the...

actually I think the relation between Kronecker and Dirac's delta is correct as the first poster says, at least for physicists. See http://bado-shanai.net/Platonic%20Dream/pdDiracDelta.htm for the proof.

Thanks very much! so to see if I understand, the n=4 determinant can be written as det A=(p14-6p12p2+3p22+8p1p3-6p4)/24 where pi=Tr (Ai) ...right?

for dimension 2, the following relation between determinant and trace of a square matrix A is true: det A=((Tr A)2-Tr (A2))/2 for dimension 3 a similar identity can be found in http://en.wikipedia.org/wiki/Determinant Does anyone know the generalization to dimension 4 ? lukluk