Hager [4] reviewed the formulae proposed by Sherman-Morrison and Woodbury that relate the

inverse of a matrix after a small-rank perturbation to the inverse of the original matrix.

Zhao, "An efficient computation of generalized

inverse of a matrix," Applied Mathematics and Computation, vol.

Wei, "Iterative methods for the Drazin

inverse of a matrix with a complex spectrum," Applied Mathematics and Computation, vol.

This stage is the

inverse of a matrix multiplication by constants in the encryption process.

Recall that the Moore-Penrose

inverse of a matrix A [member of] [C.sup.mxn] is a matrix X [member of] [C.sup.nxm] which satisfies

Where the matrix O = AT-AT BB+ and (OA) + represent the Moore-Penrose generalized

inverse of a matrix (OA).

Schreiber, "An improved Newton iteration for the generalized

inverse of a matrix, with applications," SIAM Journal on Scientific and Statistical Computing, vol.

Schreiber, "An improved Newton iteration for the generalized

inverse of a matrix, with applications," SIAM: Journal on Scientific and Statistical Computing, vol.

Secondary school teachers may use this activity to consolidate their students' learning of certain concepts of matrices such as the algorithm for matrix multiplication and the concept of the multiplicative

inverse of a matrix.

Subroutines for Testing Programs that Computer the Generalized

Inverse of a Matrix. 12,3 (Sept.

The case q = -1, which leads to estimates of the trace of the

inverse of a matrix, was studied in [4]; on this problem, see [10].

Structure of the

Inverse of a Matrix. The sparsity structure of the inverse of a square, non-singular matrix is determined by the path structure of the directed graph of the matrix.