Matrix square root

Roofit and RooStats
1

Hi rooters,

could someone please tell me if there is a way to calculate the square root of a 2x2 matrix
in root?

cheers

Mark

2

There are several ways to define the square root of a (symmetric) matrix.
Maybe you could specify more precisely what you are looking for?

Perhaps the class TMatrixDSymEigen is of use. It does a decomposition S = V D V’
where V is orthogonal and D is diagonal. Calculating the square root of D is then easy.

3

Sorry about that, let me be more specific.

I want to calculate the square root of a 2x2 hermitian matrix. So the TMatrixDSymEigen class would be fine for my purposes if it could be used to diagonalize a hermitian matrix. But it seems that root can only work with real matrices is this correct? I could probably decompose the problem into real and imaginary parts to calculate this, but I thought I should see if there is a more user friendly method before I worked out the details.

The exact calculation that I would like to perform is to calculate the Fidelity of a 2x2 density matrix. This is defined as:
A = sqrt©
Fidelity = Tr(sqrt(A.B.A))
where C,B are 2x2 hermitian matrices which are positive semi-definite so have eigenvalues between [0,1].

thanks again

Mark