Propagation of errors for matrix inversion

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 x 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. (C) 2000 Elsevier Science B.V. All rights reserved.