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...
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.
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