Bott-Duffin weak group inverse of matrices

Abstract

The paper introduces the concept of Bott-Duffin weak group inverse (in short, BDWG-inverse) of a square matrix with respect to subspace. We study some properties, representations and characterizations of the BDWG-inverse. Finally, we use this inverse to solve some restricted linear equations, restricted matrix equations and determine the solution to one of minimization problems in the Frobenius norm.