The factor-based Portfolio Expected Risks:C = X*F*X' + Ewhere C is an nxn matrix of asset return covariances, F is an mxm matrix of factor return covariances, X is nxm matrix of of factor loadings and E is nxn matrix of the specific return convariances. Consider m << n.I am trying to create characteristic portfolios which requires inv(C), the inverse of the matrix C. I am wondering if there is any way to obtain the inverse of C by inverting F and then manipulating X by multiplying by a constant k or a vector?? This will save computation time because vector multiplication and F is much smaller than C so inverting F is faster than inverting C.Any help will be appreciated.