MATRIX INVERSION BY THE ANNIHILATION OF RANK

can be readily verified, and provides a method of finding the inverse of a matrix which differs from a matrix of known inverse by a matrix of raiik unity. Equation (1) was originally derived by Sherman and Morrison [1], used by Bartlett [2], and generalized by Woodbury [3], as reported by Householder [4]. Now, since an arbitrary matrix can obviously be written as a finite sum of matrices of rank one, it is perfectly clear that one can, by repeated application of (1) invert an arbitrary nonsingular matrix. To be specific, suppose that the given matrix B has been written in the form (2) B = D + ?Z=i_ vit, where D is a nonsingular diagonal matrix. Defining the partial sum inverse