Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as b...

An efficient formula is developed for computing the inverse of a given matrix perturbed by any diverting matrix. The matrix entries may be scattering within this diverting matrix. © 2005 Elsevier Ltd. All rights reserved.

Department of Computer Science, K.U.Leuven Celestijnenlaan 200A B-3001 Heverlee, Belgium In this talk we investigate some matrix structures on Cn×n that have a good behaviour under matrix inversion. The first kind of structure is strongly related to low displacement rank structure. The second kind of structure deals with certain low rank submatrices. In this case, it can be shown that also the ...

In this paper we present different Monte Carlo algorithms to obtain inverse matrix. Here, we first determine two algorithms and describe their restrictions to be applicable for computing the inversion of a nonsingular matrix. Then, we establish an efficient algorithm to obtain approximate inversion of an arbitrary nonsingular matrix. This algorithm obtain an accurate inversion when the other tw...

With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber network containing three nodes and operating at telecomm wavelength. For an NxN matrix, ...