In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.

In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.

This note is a supplement to some recent work of R.B. Bapat on Moore-Penrose inverses of set inclusion matrices. Among other things Bapat constructs these inverses (in case of existence) forH(s, k) mod p, p an arbitrary prime, 0 ≤ s ≤ k ≤ v − s. Here we restrict ourselves to p = 2. We give conditions for s, k which are easy to state and which ensure that the Moore-Penrose inverse of H(s, k) mod...

Introduction. For a real m×n matrix A, the Moore–Penrose inverse A+ is the unique n×m matrix that satisfies the following four properties: AAA = A , AAA = A , (A+A)T = AA , (AA+)T = AA (see [1], for example). If A is a square nonsingular matrix, then A+ = A−1. Thus, the Moore–Penrose inversion generalizes ordinary matrix inversion. The idea of matrix generalized inverse was first introduced in ...

The acquisition of a discrete-time signal is an important part compressive sensing problem. A high-accuracyalgorithm that could bring better recovery performance often called for. In this work, two thresholding algorithms involve soft decision are proposed using the Moore-Penrose inverse. Numerical examples conducted and illustrate in optimal case, both methods consume computational time same l...

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for ...

In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or p...

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. As...