Hello, my name is Ramon and I am new to Mathematica and having some trouble using it for my Master's project. I know Mathematica has the functionality to do what I am after by I cannot get it to work.

As part of a project in numerical analysis of neuronal dynamical systems, I need to calculate a Matrix integral which represents the covariance of a stochastic harmonic oscillator and I do not know the syntax and everything I tried has not worked.

I have a matrix:

A={{b,d},{gf,-f}}

b,d,g,f are all real numbers and constants. I need to calculate the exponential matrix of A(x-s) where x is going to be the integration variable later on.

E=MatrixExp[A(x-s)]//MatrixForm

I also have a matrix S with the noise

S={{u,0},{0,v}}

I need to calculate the integrand

I=E*(S*Transpose(S))*Transpose(E)

And then integrate each component of this over the range 0,t. This will give me my covariance matrix. I can calculate the exponential matrix, but after that, nothing seems to work. Even if I try simple operations such as squaring my matrix E, it does not give me the right output. It gives me things like the whole matrix with a power 2 in the corner. Transposing doesn't work either. I think the problem might be that it does not know that the constants I am giving are just real numbers, but I do not know how to fix this. Some help would be most appreciated.