In this paper, we propose an approach to solving for an inverse problem. We try to evaluate a unique solution of an inverse problem by means of the weighted inverse matrix. We have applied our weighted inverse matrix method to searching for the electric field source and Demonstrating the three dimensional electric field distributions. As a result, we have succeeded in evaluating the unique elec...

This paper presents a full rank factorization of a 2 × 2 block matrix without any restriction concerning the group inverse. Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inver...

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a matrix in our class and give an algorithm for recovering this matrix from the spectral function. The reconstructive algorithm is applicable to matrices which cann...