Propagation of Errors for Matrix Inversion

Abstract

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable.

18 pages, 4 figures, figure 4 contains two eps files

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• Measurements of the branching fractions of the inclusive decays $D^0(D^{+})\to {\pi }^{+}{\pi }^{+}{\pi }^{-}X$